# First checking if I have the packages I need, and installing if not
list.of.packages <- c("tidyverse", "gplots", "RColorBrewer", "networkD3", "vegan", "rstatix", 
                      "ggalluvial", "gridExtra", "propr", "patchwork", "phyloseq", "dplyr", 
                      "VennDiagram", "plyr", "data.table", "vsn", "pheatmap", "ggpubr", 
                      "microbiome", "rmarkdown", "mixOmics", "NetCoMi", "igraph", "randomForest", 
                      "caret", "pdp", "rstatix")
new.packages <- list.of.packages[!(list.of.packages %in% installed.packages()[,"Package"])]
if(length(new.packages)) install.packages(new.packages)

# Installing some separately:
# phyloseq
# if (!requireNamespace("BiocManager", quietly = TRUE))
# install.packages("BiocManager")

# BiocManager::install("phyloseq")

# DESeq2
# BiocManager::install("DESeq2")

# vsn
# BiocManager::install("vsn")

# Had issues installing tidyverse, so I followed this first (insttalled some dependencies from the terminal) and then it worked: https://community.rstudio.com/t/tidyverse-package-does-not-install/162507/6
library(tidyverse)
library(gplots)
library(RColorBrewer)
library(ggrepel)
library(units)
library(future) # Needed to use multiple processors
library(furrr) # Needed to use multiple processors
library(progressr) # to track the progress
library(networkD3) # for Sankey diagrams
library(vegan)
library(rstatix)
library(parallel) # for setting multiple CPUs
library(ggalluvial) # to create alluvial diagrams
library(gridExtra)
# library(propr) # to compute the proportionality metric!
library(patchwork)
library(phyloseq)
library(ggnewscale)
library(dplyr)
library(VennDiagram)
# if (!require(devtools)) install.packages("devtools")
# devtools::install_github("gaospecial/ggVennDiagram")
library(ggVennDiagram)
library(ggvenn)
library(plyr) # Needed for the ordination plots I did on my own
library(data.table) # For data wrangling
library(vsn) # For normalization
# library(psych) # Used to investigate correlations among predictors in RDA analysis, ran in vegan
library(RColorBrewer)
library(pheatmap)
library(ggpubr) # has ggarrange
# EcolUtils by Guillem Salazar
library(devtools)
# devtools::install_github("GuillemSalazar/EcolUtils")
library(EcolUtils)
# Install pairwiseAdonis
# devtools::install_github("pmartinezarbizu/pairwiseAdonis/pairwiseAdonis")
library(pairwiseAdonis)
# install.packages("remotes")
# remotes::install_github("microbiome/microbiome")
library(microbiome)
# install.packages("rmarkdown")
library(rmarkdown)
library(mixOmics)
# Installing the most important package - mixOmics!
# Install mixOmics
# BiocManager::install('mixOmics')
# library(pairwiseAdonis)

# Installing the NetCoMi package I will need for microbial networks: https://github.com/stefpeschel/NetCoMi
# install.packages("devtools")
# install.packages("BiocManager")
library(doParallel)
library(foreach)
# Install NetCoMi
# devtools::install_github("stefpeschel/NetCoMi", 
#                         dependencies = c("Depends", "Imports", "LinkingTo"),
#                         repos = c("https://cloud.r-project.org/",
#                                   BiocManager::repositories()))
library(NetCoMi)
library(igraph) # needed for the function below: read_graph
# Now installing propr - to compute proportionality metric (microbial networks)
# devtools::install_github("tpq/propr")
# library(propr)

# For random forest models:
library(randomForest)
library(caret)  # For data splitting and model evaluation
library(pdp)

# Packages I need for the map:
library(reshape2) # This is only needed for the melt funtion
library(reshape)
library(dplyr)
library(plyr)
library(data.table)
library(ggplot2)
library(rworldmap)
library(rworldxtra)
# library(ggsn)
library(sf)
library(raster)
library(terra)
# library(rgeos)
# library(maps)
# library(maptools)
library(grid)
library(miscTools)
library(stringr)
library(ggpubr)
library(plyr)
library(gridExtra) # for arranging plots

# Loading all the libraries
library(raster)
library(phyloseq)
library(tidyverse)
library(ggspatial)
library(ggrepel) # The package ggrepel offers a very flexible approach to deal with label placement (with geom_text_repel and 
# geom_label_repel), including automated movement of labels in case of overlap
# Installing AIMS packages individually
library(remotes) # Needed to install the AIMS R packages below
# remotes::install_github("https://github.com/open-AIMS/dataaimsr")
library(dataaimsr)
# remotes::install_github("https://github.com/open-AIMS/gisaimsr")
library(gisaimsr)
library(sp)

# Importing the R object
load("/home/marko-terzin/Documents/PhD/Thesis/Chapter_3_IMOS-MGD_MAGs/cleaned_code/Figure_1/Figure_1.RData")

# Setting the work directory
setwd("/home/marko-terzin/Documents/PhD/Thesis/Chapter_3_IMOS-MGD_MAGs")

Importing the metagenomics data

# Absolute counts
pMAGs_95ANI <- read.delim("/home/marko-terzin/Documents/PhD/Thesis/Chapter_3_IMOS-MGD_MAGs/from_Katherine_final_abundances/only_pMAGs/pMAGs.tsv") %>% 
  column_to_rownames("genome")
# This is after I partitioned the abundances from Katherine and removed viral contigs (IMOS_V) and mobile
# elements (IMOS_M) and euk hits (IMOS_E). This should give me 876 pMAGs95ANI, and 190 samples (46 x 4 + 3 reps (Hedley) and 3reps (Davie)). Let's double check
dim(pMAGs_95ANI)
# Cleaning column names: Remove "counts." from column names
colnames(pMAGs_95ANI) <- gsub("count\\.", "", colnames(pMAGs_95ANI))

# Importing the taxa names and MAGs stats:
pMAGs_95ANI_stats <- read.csv("~/Documents/PhD/Thesis/Chapter_3_IMOS-MGD_MAGs/from_Katherine_final_abundances/only_pMAGs/Matching_names_876_MAGs_and_5000_dRep.csv")
# This object will be needed later on when I start plotting genome size, GC and etc. But for the phyloseq object I only need the taxonomy info, so let's select the columns of interest now:
pMAGs_95ANI_stats_TAX <- pMAGs_95ANI_stats %>% 
  dplyr::select("Katherine_names_876_bins", "GTDBtk.classification..R214.") %>% 
  column_to_rownames("Katherine_names_876_bins") %>% 
  separate(col = "GTDBtk.classification..R214.",
           into = c("Domain", "Phylum", "Class", "Order", "Family", "Genus", "Species"),
           sep = ";")
### Data input ###

# Adding the metadata file!
# Metadata - where I have average values of WQ and LTMP data
# I already have it from the read-based analysis, I just made sure (manually!) it corresponds to Yun Kit's naming

# Importing the file I used for random forest models because it doesn't have naS 
metadata_IMOS_MGD_MAGs <- read.csv("~/Documents/PhD/Thesis/Chapter_3_IMOS-MGD_MAGs/metadata_for_random_forest_models.csv")
# metadata_IMOS_MGD_MAGs <- read.csv("~/Documents/PhD/Thesis/Chapter_3_IMOS-MGD_MAGs/input_data_from_Yun_Kit/metadata_IMOS_MGD_MAGs_Katherine.csv")
### Important update on 2nd June 2025: modified 21-580 manually to say it's open to fishing. Same modification in MINT_sector_manually_edited.csv

# Now adding the sector information as well
MINT_sector_manually_edited <- read.csv("~/Documents/PhD/Thesis/Chapter_3_IMOS-MGD_MAGs/MINT_sector_manually_edited.csv")

# Merging:
metadata_IMOS_MGD_MAGs <- left_join(metadata_IMOS_MGD_MAGs,
                                    MINT_sector_manually_edited %>% 
                                    dplyr::select("Sample_ID", "SECTOR")
                                    )
# Adding sector value for two sites where it's missing for some reason...
# Dor 21-580:
metadata_IMOS_MGD_MAGs$SECTOR <- ifelse(grepl("21580_", metadata_IMOS_MGD_MAGs$Sample_ID),
                                        "SW", metadata_IMOS_MGD_MAGs$SECTOR)
# For St Crispin:
metadata_IMOS_MGD_MAGs$SECTOR <- ifelse(grepl("stcrispin_", metadata_IMOS_MGD_MAGs$Sample_ID),
                                        "CA", metadata_IMOS_MGD_MAGs$SECTOR)

# Now adding the WQ medians!
# WQ_medians_per_reef <- read.csv("~/Documents/PhD/Thesis/Chapter_3_IMOS-MGD_MAGs/input_data_from_Yun_Kit/metadata_WQ_medians_per_reef.csv")
# Merging
# metadata_IMOS_MGD_MAGs <- left_join(metadata_IMOS_MGD_MAGs, WQ_medians_per_reef)

# Merging into a phyloseq object
OTU = otu_table(pMAGs_95ANI, taxa_are_rows = TRUE)
TAX = tax_table(as.matrix(pMAGs_95ANI_stats_TAX))
pMAGs_95ANI_phyloseq <- phyloseq(OTU, TAX)

# Before merging into the same phyloseq object, make sure the Sample IDs in metadata and OTU objects are in the same order
OTU_Sample_IDs <- as.data.frame(colnames(OTU))
colnames(OTU_Sample_IDs) <- "Sample_ID"
# Making sure samples are ordered in the same way
metadata_IMOS_MGD_MAGs <- left_join(OTU_Sample_IDs, metadata_IMOS_MGD_MAGs)

# Just changing the sectors so that they are ordered from North to South
# Cape Grenville sector
# Princess Charlotte Bay sector
# Cairns sector
# Innisfail sector
# Townsville sector
# Swains sector
# Capricorn Bunker sector

metadata_IMOS_MGD_MAGs <- metadata_IMOS_MGD_MAGs %>%
  mutate(SECTOR_N_S = recode(SECTOR,
                              CG = "01_Cape_Grenville",
                              PC = "02_Princess_Charlotte_bay",
                              CA = "03_Cairns",
                              IN = "04_Innisfail",
                              TO = "05_Townsville",
                              SW = "06_Swains",
                              CB = "07_Capricorn_Bunker"))

# Preparing the metadata to merge with the phyloseq object
sampledata <- metadata_IMOS_MGD_MAGs

# 1. Ensure we have the exact same samples in both datasets
otu_samples <- colnames(otu_table(pMAGs_95ANI_phyloseq))
sampledata <- sampledata %>% 
  filter(Sample_ID %in% otu_samples) %>% 
  arrange(match(Sample_ID, otu_samples))

# 2. Verify dimensions match exactly
if(nrow(sampledata) != length(otu_samples)) {
  stop(paste("Sample count mismatch: Metadata has", nrow(sampledata),
             "samples, OTU table has", length(otu_samples)))
}

# 3. Create sample_data object with proper row names
sampledata <- sample_data(
  data.frame(
    sampledata,
    row.names = sampledata$Sample_ID,  # Explicit row names
    stringsAsFactors = FALSE
  )
)

# 4. Final validation checks
print("First 5 sample names in metadata:")
## [1] "First 5 sample names in metadata:"
print(head(rownames(sampledata)))
## [1] "11049_1__BBG5542_21S000057" "11049_2__BBG5543_21S000444"
## [3] "11049_3__BBG5544_21S000445" "11049_4__BBG5545_21S000446"
## [5] "11162_1__BBG5534"           "11162_2__BBG5535"
print("First 5 sample names in OTU table:")
## [1] "First 5 sample names in OTU table:"
print(head(colnames(otu_table(pMAGs_95ANI_phyloseq))))
## [1] "11049_1__BBG5542_21S000057" "11049_2__BBG5543_21S000444"
## [3] "11049_3__BBG5544_21S000445" "11049_4__BBG5545_21S000446"
## [5] "11162_1__BBG5534"           "11162_2__BBG5535"
print("Any NA values in Sample_ID?")
## [1] "Any NA values in Sample_ID?"
print(any(is.na(sampledata$Sample_ID)))
## [1] FALSE
if(!validObject(sampledata)) {
  print("Sample data validation failed. Structure:")
  str(sampledata)
  stop("Invalid sample_data object")
}

# 5. Merge with phyloseq
pMAGs_95ANI_phyloseq <- merge_phyloseq(pMAGs_95ANI_phyloseq, sampledata)
### Data Normalisation - Center Log Ratio (CLR) transformation ###

# CLR is the normalisation method suggested by the mixOmics R package for microbial data - a way to address missing values that are characteristic of microbial datasets. I need to remove missing values before doing the CLR normalisation - The geometric mean cannot be determined for sparse data without deleting, replacing or estimating the 0 count values. So I am introducing pseudo counts

### Tutorial used: http://mixomics.org/mixmc/mixmc-preprocessing/

# Checking if there are any zeros - BEFORE adding pseudocounts
sum(which(pMAGs_95ANI_phyloseq@otu_table == 0))
# Pseudocounts - replacing all zero vals with 1; 
pMAGs_95ANI_phyloseq@otu_table <- pMAGs_95ANI_phyloseq@otu_table + 1
# Checking if there are any zeros - AFTER adding pseudocounts
sum(which(pMAGs_95ANI_phyloseq@otu_table == 0))
# All good! No NAs after introducing pseudocounts

### Now I can CLR transform:
# All data, but the correct thing should be each sector separately
pMAGs_95ANI_phyloseq_clr <- microbiome::transform(pMAGs_95ANI_phyloseq, transform = "clr")

# CLR within each sector - use this object for MINT:
# 1. Extract sample data and sectors
sector_info <- sample_data(pMAGs_95ANI_phyloseq)$SECTOR_N_S
sectors <- unique(sector_info)

# 2. Initialize an empty list to store CLR-transformed subsets
phy_clr_list <- list()

# 3. Loop through each sector, apply CLR, and store results
for (sector in sectors) {
  # Subset phyloseq by sector
  phy_subset <- subset_samples(pMAGs_95ANI_phyloseq, SECTOR_N_S == sector)
  
  # Apply CLR to the subset (with pseudo-count to avoid zeros)
  phy_subset_clr <- microbiome::transform(phy_subset, transform = "clr")
  
  # Store in list
  phy_clr_list[[sector]] <- phy_subset_clr
}

# 4. Merge all sectors back into one phyloseq object
pMAGs_95ANI_phyloseq_CLR_per_sector <- do.call(merge_phyloseq, phy_clr_list)

# 5. Verify the output
head(otu_table(pMAGs_95ANI_phyloseq_CLR_per_sector))  # Should show CLR values
### IMPORTANT: use pMAGs_95ANI_phyloseq_CLR_per_sector only for MINT!!

What are the main clustering patterns across our samples? PCA - Principal Components Analysis

Principal Components Analysis (PCA) was applied in an R package mixOmics (Rohart et al. 2017b) as an unsupervised approach to visualise the main clustering patterns between reef sites based on microbial community profiles The number of optimal PCA components was determined using the tune.pca() function in mixOmics (Rohart et al. 2017b).

# This is a matrix with OTU counts - raw, with pseudocounts introduced!
MAGs <- as.data.frame(pMAGs_95ANI_phyloseq_clr@otu_table)
MAGs <- t(MAGs)
# Check dimensions of data
dim(MAGs)
class(MAGs)

# Minimal code - mixOmics, PCA
result.pca <- pca(MAGs)
pca_MAGs_95 <- plotIndiv(result.pca,
          group = sample_data(pMAGs_95ANI_phyloseq_clr)$Sampling_trip,
          title = 'PCA | 876 IMOS GBR-MGD MAGs - (95% ANI)',
          legend = T,
          ellipse = TRUE,
          ind.names = F,
          col.per.group =c("indianred", # Sampling trip 1
                "indianred4", # Sampling trip 2 
                "red3", # Sampling trip 3
                "slateblue"), # Sampling trip 4
          legend.title = 'Sampling trip'
          )
Main clustering patterns of seawater microbial communities. The PCA ordination plots show clear differences between microbial communities sampled during the summer/wet season (red) and winter/dry season (blue), with 50% of variance being attributable to dimension 1. Samples collected in the peak of summer (Trip 3) additionally separate from early summer sampling (Trips 1 and 2) on PCA dimension 2.

Main clustering patterns of seawater microbial communities. The PCA ordination plots show clear differences between microbial communities sampled during the summer/wet season (red) and winter/dry season (blue), with 50% of variance being attributable to dimension 1. Samples collected in the peak of summer (Trip 3) additionally separate from early summer sampling (Trips 1 and 2) on PCA dimension 2.

# I will need this later for plotting

# Defining MAG names - full taxonomy
MAGs.full.name.and.OTU <- left_join(otu_table(pMAGs_95ANI_phyloseq_clr) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU"),
                            tax_table(pMAGs_95ANI_phyloseq_clr) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU")) %>%
  tidyr::unite(taxonomy, c(OTU, Domain, Class, Order, Family, Genus, Species), sep = "; ") # Adding Taxonomy info
## Joining, by = "OTU"
MAGs.full.name.and.OTU <- as.character(MAGs.full.name.and.OTU$taxonomy)

# Exporting the names of taxa now, and making them short - easier plotting!
MAGs.name.short <- left_join(otu_table(pMAGs_95ANI_phyloseq_clr) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU"),
                            tax_table(pMAGs_95ANI_phyloseq_clr) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU")) %>%
  tidyr::unite(taxonomy, c(Class, Order, Family, Genus, Species), sep = "; ") # Adding Taxonomy info
## Joining, by = "OTU"
MAGs.name.short <- as.character(MAGs.name.short$taxonomy)

MAGs.name.super.short <- left_join(otu_table(pMAGs_95ANI_phyloseq_clr) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU"),
                            tax_table(pMAGs_95ANI_phyloseq_clr) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU")) %>%
  tidyr::unite(taxonomy, c(Family, Genus, Species), sep = "; ") # Adding Taxonomy info
## Joining, by = "OTU"
MAGs.name.super.short <- as.character(MAGs.name.super.short$taxonomy)

Can we distinguish between no-take and take zones?

PCA - coloring based on reef protection

pca_open_closed <- plotIndiv(result.pca,
          group = sample_data(pMAGs_95ANI_phyloseq_clr)$Open_or_Closed_to_fishing,
          pch = as.factor(sample_data(pMAGs_95ANI_phyloseq_clr)$SECTOR),
          title = 'PCA | 876 IMOS-MGD MAGs (95% ANI)',
          legend = T,
          ellipse = T,
          ind.names = F,
          col.per.group = c("seagreen3", # Closed to fishing
                            "steelblue4"), # open to fishing
          legend.title = 'Reef Protection Status'
          )

PCA on its own does not discriminate between zones, and sites are clustering based on geographic proximity (i.e. sector) and time (i.e. sampling trip). Will (sPLS-DA) improve the separation between zones as a supervised approach?

Optimal Number of components in PLS-DA

The perf() function evaluates the performance of PLS-DA - i.e., its ability to rightly classify ‘new’ samples into their category (no-take and take zones) using repeated cross-validation. We initially choose a large number of components (here ncomp = 10) and assess the model as we gradually increase the number of components. Here we use 4-fold CV repeated 50 times.

plsda.open.closed <- mixOmics::plsda(X = MAGs,
                     Y = metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing,
                     ncomp = 10)
perf.plsda.open.closed <- perf(plsda.open.closed,
                               validation = 'Mfold',
                               folds = 4,
                               progressBar = TRUE,  # Set to TRUE to track progress
                               nrepeat = 50)         # We suggest nrepeat = 50 (at least)
## 
## comp 1 
##   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |==                                                                    |   4%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |=========                                                             |  14%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |================                                                      |  24%  |                                                                              |=================                                                     |  24%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |=======================                                               |  34%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  40%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |==============================                                        |  44%  |                                                                              |===============================                                       |  44%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |=====================================                                 |  54%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  56%  |                                                                              |========================================                              |  57%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |============================================                          |  64%  |                                                                              |=============================================                         |  64%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |===================================================                   |  74%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  80%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |==========================================================            |  84%  |                                                                              |===========================================================           |  84%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |=================================================================     |  94%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================| 100%
## comp 2 
##   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |==                                                                    |   4%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |=========                                                             |  14%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |================                                                      |  24%  |                                                                              |=================                                                     |  24%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |=======================                                               |  34%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  40%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |==============================                                        |  44%  |                                                                              |===============================                                       |  44%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |=====================================                                 |  54%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  56%  |                                                                              |========================================                              |  57%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |============================================                          |  64%  |                                                                              |=============================================                         |  64%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |===================================================                   |  74%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  80%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |==========================================================            |  84%  |                                                                              |===========================================================           |  84%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |=================================================================     |  94%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================| 100%
## comp 3 
##   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |==                                                                    |   4%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |=========                                                             |  14%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |================                                                      |  24%  |                                                                              |=================                                                     |  24%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |=======================                                               |  34%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  40%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |==============================                                        |  44%  |                                                                              |===============================                                       |  44%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |=====================================                                 |  54%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  56%  |                                                                              |========================================                              |  57%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |============================================                          |  64%  |                                                                              |=============================================                         |  64%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |===================================================                   |  74%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  80%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |==========================================================            |  84%  |                                                                              |===========================================================           |  84%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |=================================================================     |  94%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================| 100%
## comp 4 
##   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |==                                                                    |   4%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |=========                                                             |  14%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |================                                                      |  24%  |                                                                              |=================                                                     |  24%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |=======================                                               |  34%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  40%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |==============================                                        |  44%  |                                                                              |===============================                                       |  44%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |=====================================                                 |  54%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  56%  |                                                                              |========================================                              |  57%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |============================================                          |  64%  |                                                                              |=============================================                         |  64%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |===================================================                   |  74%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  80%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |==========================================================            |  84%  |                                                                              |===========================================================           |  84%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |=================================================================     |  94%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================| 100%
## comp 5 
##   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |==                                                                    |   4%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |=========                                                             |  14%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |================                                                      |  24%  |                                                                              |=================                                                     |  24%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |=======================                                               |  34%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  40%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |==============================                                        |  44%  |                                                                              |===============================                                       |  44%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |=====================================                                 |  54%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  56%  |                                                                              |========================================                              |  57%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |============================================                          |  64%  |                                                                              |=============================================                         |  64%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |===================================================                   |  74%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  80%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |==========================================================            |  84%  |                                                                              |===========================================================           |  84%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |=================================================================     |  94%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================| 100%
## comp 6 
##   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |==                                                                    |   4%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |=========                                                             |  14%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |================                                                      |  24%  |                                                                              |=================                                                     |  24%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |=======================                                               |  34%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  40%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |==============================                                        |  44%  |                                                                              |===============================                                       |  44%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |=====================================                                 |  54%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  56%  |                                                                              |========================================                              |  57%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |============================================                          |  64%  |                                                                              |=============================================                         |  64%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |===================================================                   |  74%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  80%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |==========================================================            |  84%  |                                                                              |===========================================================           |  84%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |=================================================================     |  94%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================| 100%
## comp 7 
##   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |==                                                                    |   4%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |=========                                                             |  14%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |================                                                      |  24%  |                                                                              |=================                                                     |  24%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |=======================                                               |  34%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  40%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |==============================                                        |  44%  |                                                                              |===============================                                       |  44%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |=====================================                                 |  54%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  56%  |                                                                              |========================================                              |  57%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |============================================                          |  64%  |                                                                              |=============================================                         |  64%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |===================================================                   |  74%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  80%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |==========================================================            |  84%  |                                                                              |===========================================================           |  84%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |=================================================================     |  94%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================| 100%
## comp 8 
##   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |==                                                                    |   4%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |=========                                                             |  14%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |================                                                      |  24%  |                                                                              |=================                                                     |  24%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |=======================                                               |  34%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  40%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |==============================                                        |  44%  |                                                                              |===============================                                       |  44%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |=====================================                                 |  54%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  56%  |                                                                              |========================================                              |  57%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |============================================                          |  64%  |                                                                              |=============================================                         |  64%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |===================================================                   |  74%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  80%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |==========================================================            |  84%  |                                                                              |===========================================================           |  84%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |=================================================================     |  94%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================| 100%
## comp 9 
##   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |==                                                                    |   4%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |=========                                                             |  14%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |================                                                      |  24%  |                                                                              |=================                                                     |  24%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |=======================                                               |  34%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  40%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |==============================                                        |  44%  |                                                                              |===============================                                       |  44%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |=====================================                                 |  54%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  56%  |                                                                              |========================================                              |  57%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |============================================                          |  64%  |                                                                              |=============================================                         |  64%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |===================================================                   |  74%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  80%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |==========================================================            |  84%  |                                                                              |===========================================================           |  84%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |=================================================================     |  94%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================| 100%
## comp 10 
##   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |==                                                                    |   4%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |=========                                                             |  14%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |================                                                      |  24%  |                                                                              |=================                                                     |  24%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |=======================                                               |  34%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  40%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |==============================                                        |  44%  |                                                                              |===============================                                       |  44%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |=====================================                                 |  54%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  56%  |                                                                              |========================================                              |  57%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |============================================                          |  64%  |                                                                              |=============================================                         |  64%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |===================================================                   |  74%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  80%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |==========================================================            |  84%  |                                                                              |===========================================================           |  84%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |=================================================================     |  94%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================| 100%
# Plot
plot(perf.plsda.open.closed, sd = TRUE, legend.position = 'horizontal')
Tuning the number of components in PLS-DA on the IMOS-MGD MAG data (876 MAGs, drep at 95% ANI). For each component, repeated cross-validation (50 ×4−fold CV) is used to evaluate the PLS-DA classification performance (overall and balanced error rate BER, and for each type of prediction distance: max.dist, centroids.dist and mahalanobis.dist) to discriminate between no-take and take zones based on the seawater microbiome. Bars show the standard deviation across the repeated folds. The plot shows that the error rate keeps dropping as we increase the number of components, but I will retain 2 dimensions in the final PLS-DA model (1) to avoid overfitting, and because (2) I am only aiming to discriminate between two categorical outcomes.

Tuning the number of components in PLS-DA on the IMOS-MGD MAG data (876 MAGs, drep at 95% ANI). For each component, repeated cross-validation (50 ×4−fold CV) is used to evaluate the PLS-DA classification performance (overall and balanced error rate BER, and for each type of prediction distance: max.dist, centroids.dist and mahalanobis.dist) to discriminate between no-take and take zones based on the seawater microbiome. Bars show the standard deviation across the repeated folds. The plot shows that the error rate keeps dropping as we increase the number of components, but I will retain 2 dimensions in the final PLS-DA model (1) to avoid overfitting, and because (2) I am only aiming to discriminate between two categorical outcomes.

This is odd because the model keeps adding components, but 1-2 PCs should be enough for two outcomes (categorical).

Final PLS-DA model

We now run our final PLS-DA model that includes 2 components:

final.plsda.open.closed <- mixOmics::plsda(X = MAGs,
                     Y = metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing,
                     ncomp = 2)
pls.da.open.closed <- plotIndiv(final.plsda.open.closed,
          ind.names = FALSE,
          group = sample_data(pMAGs_95ANI_phyloseq_clr)$Open_or_Closed_to_fishing,
#          pch.levels = sample_data(pMAGs_95ANI_phyloseq_clr)$Sampling_trip,
          pch = as.factor(sample_data(pMAGs_95ANI_phyloseq_clr)$Sampling_trip),
          legend=TRUE,
          col.per.group = c("seagreen3", # Closed to fishing
                            "steelblue4"), # open to fishing
          legend.title = 'Reef Protection Status',
          comp=c(1,2),
          ellipse = TRUE, 
          title = 'PLS-DA on IMOS-MGD MAGs (876, 95% ANI derep)',
#          X.label = 'PLS-DA comp 1',
#          Y.label = 'PLS-DA comp 2',
)

pls.da.open.closed <- plotIndiv(final.plsda.open.closed,
          ind.names = FALSE,
          group = sample_data(pMAGs_95ANI_phyloseq_clr)$Sampling_trip,
#          pch.levels = sample_data(pMAGs_95ANI_phyloseq_clr)$Sampling_trip,
          pch = as.factor(sample_data(pMAGs_95ANI_phyloseq_clr)$Open_or_Closed_to_fishing),
          legend=TRUE,
col.per.group =c("indianred", # Sampling trip 1
                "indianred4", # Sampling trip 2 
                "red3", # Sampling trip 3
                "slateblue"), # Sampling trip 4
          legend.title = 'Sampling trip',
          comp=c(1,2),
          ellipse = TRUE, 
          title = 'PLS-DA on IMOS-MGD MAGs (876, 95% ANI derep)',
#          X.label = 'PLS-DA comp 1',
#          Y.label = 'PLS-DA comp 2',
)

We can observe improved clustering according to reef protection status (top), compared with PCA. This is to be expected since the PLS-DA model includes the class information of each sample, and aims to discriminate between them. From the plotIndiv() function, we observe some discrimination between no-take and take zones mostly on component 1 (x-axis), however we can still see the trip effect (bottom). The axis labels indicate the amount of variation explained per component, however, the interpretation of this amount is not as important as in PCA, as PLS-DA aims to maximise the covariance between components associated to X (predictor dataset, i.e. the 876 IMOS-MGD MAGs) and Y (categorical “response”, i.e. no-take and take zones), rather than the variance of X (done in PCA).

Classification performance of the final model

We can rerun a more extensive performance evaluation with more repeats for our final model:

perf.final.plsda.open.closed <- perf(final.plsda.open.closed,
                                     validation = 'Mfold',
                                     folds = 4,
                                     progressBar = TRUE, # TRUE to track progress
                                     nrepeat = 50) # we recommend 50 

Numerical outputs of interest include the final overall performance for 2 components (Ballanced error rate, max.dist):

perf.final.plsda.open.closed$error.rate$BER[, 'max.dist']
##     comp1     comp2 
## 0.3854246 0.2816495

We can also get the error rate per class across each component:

perf.final.plsda.open.closed$error.rate.class$max.dist
##       comp1     comp2
## C 0.4617582 0.2758242
## O 0.3090909 0.2874747

sPLS-DA - can we refine these clusters by selecting the most influential MAGs?

As many of the 876 MAGs in X may be noisy or uninformative to discriminate between no-take and take reefs, an sPLS-DA analysis (sparse variant) may help refine the sample clusters and select a small subset of variables relevant to discriminate each class.

Tuning the number of variables to select

We estimate the classification error rate with respect to the number of selected variables in the model with the function tune.splsda(). The tuning is being performed one component at a time inside the function and the optimal number of variables to select is automatically retrieved after each component run.

Previously, we determined the optimal number of components to be ncomp = 2 with PLS-DA. Here we set ncomp = 3 to further assess if this would be the case for a sparse model, and use 4-fold cross validation repeated 50 times.

We first define a grid of keepX values. For example here, we define a fine grid at the start, and then specify a coarser, larger sequence of values:

# Grid of possible keepX values that will be tested for each comp
list.keepX <- c(1:10,  seq(20, 150, 10))
list.keepX
##  [1]   1   2   3   4   5   6   7   8   9  10  20  30  40  50  60  70  80  90 100
## [20] 110 120 130 140 150
tune.splsda.open.closed <- tune.splsda(X = MAGs,
                                       Y = metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing,
                                       ncomp = 8,
                                       progressBar = TRUE,
                                       validation = 'Mfold', 
                                       folds = 10,
                                       # dist = 'max.dist',
                                       test.keepX = list.keepX,
                                       nrepeat = 50)
## 
## comp 1 
##   |                                                                              |                                                                      |   0%  |                                                                              |                                                                      |   1%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |===                                                                   |   4%  |                                                                              |===                                                                   |   5%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |=======                                                               |  11%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |==============                                                        |  21%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |=================                                                     |  24%  |                                                                              |=================                                                     |  25%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |=====================                                                 |  31%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  39%  |                                                                              |============================                                          |  40%  |                                                                              |============================                                          |  41%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |===============================                                       |  44%  |                                                                              |===============================                                       |  45%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |===================================                                   |  51%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  57%  |                                                                              |========================================                              |  58%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |==========================================                            |  61%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |=============================================                         |  64%  |                                                                              |=============================================                         |  65%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |=================================================                     |  71%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  79%  |                                                                              |========================================================              |  80%  |                                                                              |========================================================              |  81%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |===========================================================           |  84%  |                                                                              |===========================================================           |  85%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |===============================================================       |  91%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================|  99%  |                                                                              |======================================================================| 100%
## comp 2 
##   |                                                                              |                                                                      |   0%  |                                                                              |                                                                      |   1%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |===                                                                   |   4%  |                                                                              |===                                                                   |   5%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |=======                                                               |  11%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |==============                                                        |  21%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |=================                                                     |  24%  |                                                                              |=================                                                     |  25%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |=====================                                                 |  31%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  39%  |                                                                              |============================                                          |  40%  |                                                                              |============================                                          |  41%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |===============================                                       |  44%  |                                                                              |===============================                                       |  45%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |===================================                                   |  51%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  57%  |                                                                              |========================================                              |  58%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |==========================================                            |  61%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |=============================================                         |  64%  |                                                                              |=============================================                         |  65%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |=================================================                     |  71%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  79%  |                                                                              |========================================================              |  80%  |                                                                              |========================================================              |  81%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |===========================================================           |  84%  |                                                                              |===========================================================           |  85%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |===============================================================       |  91%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================|  99%  |                                                                              |======================================================================| 100%
## comp 3 
##   |                                                                              |                                                                      |   0%  |                                                                              |                                                                      |   1%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |===                                                                   |   4%  |                                                                              |===                                                                   |   5%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |=======                                                               |  11%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |==============                                                        |  21%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |=================                                                     |  24%  |                                                                              |=================                                                     |  25%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |=====================                                                 |  31%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  39%  |                                                                              |============================                                          |  40%  |                                                                              |============================                                          |  41%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |===============================                                       |  44%  |                                                                              |===============================                                       |  45%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |===================================                                   |  51%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  57%  |                                                                              |========================================                              |  58%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |==========================================                            |  61%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |=============================================                         |  64%  |                                                                              |=============================================                         |  65%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |=================================================                     |  71%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  79%  |                                                                              |========================================================              |  80%  |                                                                              |========================================================              |  81%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |===========================================================           |  84%  |                                                                              |===========================================================           |  85%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |===============================================================       |  91%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================|  99%  |                                                                              |======================================================================| 100%
## comp 4 
##   |                                                                              |                                                                      |   0%  |                                                                              |                                                                      |   1%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |===                                                                   |   4%  |                                                                              |===                                                                   |   5%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |=======                                                               |  11%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |==============                                                        |  21%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |=================                                                     |  24%  |                                                                              |=================                                                     |  25%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |=====================                                                 |  31%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  39%  |                                                                              |============================                                          |  40%  |                                                                              |============================                                          |  41%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |===============================                                       |  44%  |                                                                              |===============================                                       |  45%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |===================================                                   |  51%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  57%  |                                                                              |========================================                              |  58%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |==========================================                            |  61%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |=============================================                         |  64%  |                                                                              |=============================================                         |  65%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |=================================================                     |  71%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  79%  |                                                                              |========================================================              |  80%  |                                                                              |========================================================              |  81%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |===========================================================           |  84%  |                                                                              |===========================================================           |  85%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |===============================================================       |  91%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================|  99%  |                                                                              |======================================================================| 100%
## comp 5 
##   |                                                                              |                                                                      |   0%  |                                                                              |                                                                      |   1%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |===                                                                   |   4%  |                                                                              |===                                                                   |   5%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |=======                                                               |  11%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |==============                                                        |  21%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |=================                                                     |  24%  |                                                                              |=================                                                     |  25%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |=====================                                                 |  31%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  39%  |                                                                              |============================                                          |  40%  |                                                                              |============================                                          |  41%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |===============================                                       |  44%  |                                                                              |===============================                                       |  45%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |===================================                                   |  51%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  57%  |                                                                              |========================================                              |  58%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |==========================================                            |  61%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |=============================================                         |  64%  |                                                                              |=============================================                         |  65%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |=================================================                     |  71%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  79%  |                                                                              |========================================================              |  80%  |                                                                              |========================================================              |  81%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |===========================================================           |  84%  |                                                                              |===========================================================           |  85%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |===============================================================       |  91%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================|  99%  |                                                                              |======================================================================| 100%
## comp 6 
##   |                                                                              |                                                                      |   0%  |                                                                              |                                                                      |   1%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |===                                                                   |   4%  |                                                                              |===                                                                   |   5%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |=======                                                               |  11%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |==============                                                        |  21%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |=================                                                     |  24%  |                                                                              |=================                                                     |  25%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |=====================                                                 |  31%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  39%  |                                                                              |============================                                          |  40%  |                                                                              |============================                                          |  41%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |===============================                                       |  44%  |                                                                              |===============================                                       |  45%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |===================================                                   |  51%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  57%  |                                                                              |========================================                              |  58%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |==========================================                            |  61%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |=============================================                         |  64%  |                                                                              |=============================================                         |  65%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |=================================================                     |  71%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  79%  |                                                                              |========================================================              |  80%  |                                                                              |========================================================              |  81%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |===========================================================           |  84%  |                                                                              |===========================================================           |  85%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |===============================================================       |  91%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================|  99%  |                                                                              |======================================================================| 100%
## comp 7 
##   |                                                                              |                                                                      |   0%  |                                                                              |                                                                      |   1%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |===                                                                   |   4%  |                                                                              |===                                                                   |   5%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |=======                                                               |  11%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |==============                                                        |  21%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |=================                                                     |  24%  |                                                                              |=================                                                     |  25%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |=====================                                                 |  31%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  39%  |                                                                              |============================                                          |  40%  |                                                                              |============================                                          |  41%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |===============================                                       |  44%  |                                                                              |===============================                                       |  45%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |===================================                                   |  51%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  57%  |                                                                              |========================================                              |  58%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |==========================================                            |  61%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |=============================================                         |  64%  |                                                                              |=============================================                         |  65%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |=================================================                     |  71%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  79%  |                                                                              |========================================================              |  80%  |                                                                              |========================================================              |  81%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |===========================================================           |  84%  |                                                                              |===========================================================           |  85%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |===============================================================       |  91%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================|  99%  |                                                                              |======================================================================| 100%
## comp 8 
##   |                                                                              |                                                                      |   0%  |                                                                              |                                                                      |   1%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |===                                                                   |   4%  |                                                                              |===                                                                   |   5%  |                                                                              |====                                                                  |   5%  |                                                                              |====                                                                  |   6%  |                                                                              |=====                                                                 |   7%  |                                                                              |=====                                                                 |   8%  |                                                                              |======                                                                |   8%  |                                                                              |======                                                                |   9%  |                                                                              |=======                                                               |   9%  |                                                                              |=======                                                               |  10%  |                                                                              |=======                                                               |  11%  |                                                                              |========                                                              |  11%  |                                                                              |========                                                              |  12%  |                                                                              |=========                                                             |  12%  |                                                                              |=========                                                             |  13%  |                                                                              |==========                                                            |  14%  |                                                                              |==========                                                            |  15%  |                                                                              |===========                                                           |  15%  |                                                                              |===========                                                           |  16%  |                                                                              |============                                                          |  17%  |                                                                              |============                                                          |  18%  |                                                                              |=============                                                         |  18%  |                                                                              |=============                                                         |  19%  |                                                                              |==============                                                        |  19%  |                                                                              |==============                                                        |  20%  |                                                                              |==============                                                        |  21%  |                                                                              |===============                                                       |  21%  |                                                                              |===============                                                       |  22%  |                                                                              |================                                                      |  22%  |                                                                              |================                                                      |  23%  |                                                                              |=================                                                     |  24%  |                                                                              |=================                                                     |  25%  |                                                                              |==================                                                    |  25%  |                                                                              |==================                                                    |  26%  |                                                                              |===================                                                   |  27%  |                                                                              |===================                                                   |  28%  |                                                                              |====================                                                  |  28%  |                                                                              |====================                                                  |  29%  |                                                                              |=====================                                                 |  29%  |                                                                              |=====================                                                 |  30%  |                                                                              |=====================                                                 |  31%  |                                                                              |======================                                                |  31%  |                                                                              |======================                                                |  32%  |                                                                              |=======================                                               |  32%  |                                                                              |=======================                                               |  33%  |                                                                              |========================                                              |  34%  |                                                                              |========================                                              |  35%  |                                                                              |=========================                                             |  35%  |                                                                              |=========================                                             |  36%  |                                                                              |==========================                                            |  37%  |                                                                              |==========================                                            |  38%  |                                                                              |===========================                                           |  38%  |                                                                              |===========================                                           |  39%  |                                                                              |============================                                          |  39%  |                                                                              |============================                                          |  40%  |                                                                              |============================                                          |  41%  |                                                                              |=============================                                         |  41%  |                                                                              |=============================                                         |  42%  |                                                                              |==============================                                        |  42%  |                                                                              |==============================                                        |  43%  |                                                                              |===============================                                       |  44%  |                                                                              |===============================                                       |  45%  |                                                                              |================================                                      |  45%  |                                                                              |================================                                      |  46%  |                                                                              |=================================                                     |  47%  |                                                                              |=================================                                     |  48%  |                                                                              |==================================                                    |  48%  |                                                                              |==================================                                    |  49%  |                                                                              |===================================                                   |  49%  |                                                                              |===================================                                   |  50%  |                                                                              |===================================                                   |  51%  |                                                                              |====================================                                  |  51%  |                                                                              |====================================                                  |  52%  |                                                                              |=====================================                                 |  52%  |                                                                              |=====================================                                 |  53%  |                                                                              |======================================                                |  54%  |                                                                              |======================================                                |  55%  |                                                                              |=======================================                               |  55%  |                                                                              |=======================================                               |  56%  |                                                                              |========================================                              |  57%  |                                                                              |========================================                              |  58%  |                                                                              |=========================================                             |  58%  |                                                                              |=========================================                             |  59%  |                                                                              |==========================================                            |  59%  |                                                                              |==========================================                            |  60%  |                                                                              |==========================================                            |  61%  |                                                                              |===========================================                           |  61%  |                                                                              |===========================================                           |  62%  |                                                                              |============================================                          |  62%  |                                                                              |============================================                          |  63%  |                                                                              |=============================================                         |  64%  |                                                                              |=============================================                         |  65%  |                                                                              |==============================================                        |  65%  |                                                                              |==============================================                        |  66%  |                                                                              |===============================================                       |  67%  |                                                                              |===============================================                       |  68%  |                                                                              |================================================                      |  68%  |                                                                              |================================================                      |  69%  |                                                                              |=================================================                     |  69%  |                                                                              |=================================================                     |  70%  |                                                                              |=================================================                     |  71%  |                                                                              |==================================================                    |  71%  |                                                                              |==================================================                    |  72%  |                                                                              |===================================================                   |  72%  |                                                                              |===================================================                   |  73%  |                                                                              |====================================================                  |  74%  |                                                                              |====================================================                  |  75%  |                                                                              |=====================================================                 |  75%  |                                                                              |=====================================================                 |  76%  |                                                                              |======================================================                |  77%  |                                                                              |======================================================                |  78%  |                                                                              |=======================================================               |  78%  |                                                                              |=======================================================               |  79%  |                                                                              |========================================================              |  79%  |                                                                              |========================================================              |  80%  |                                                                              |========================================================              |  81%  |                                                                              |=========================================================             |  81%  |                                                                              |=========================================================             |  82%  |                                                                              |==========================================================            |  82%  |                                                                              |==========================================================            |  83%  |                                                                              |===========================================================           |  84%  |                                                                              |===========================================================           |  85%  |                                                                              |============================================================          |  85%  |                                                                              |============================================================          |  86%  |                                                                              |=============================================================         |  87%  |                                                                              |=============================================================         |  88%  |                                                                              |==============================================================        |  88%  |                                                                              |==============================================================        |  89%  |                                                                              |===============================================================       |  89%  |                                                                              |===============================================================       |  90%  |                                                                              |===============================================================       |  91%  |                                                                              |================================================================      |  91%  |                                                                              |================================================================      |  92%  |                                                                              |=================================================================     |  92%  |                                                                              |=================================================================     |  93%  |                                                                              |==================================================================    |  94%  |                                                                              |==================================================================    |  95%  |                                                                              |===================================================================   |  95%  |                                                                              |===================================================================   |  96%  |                                                                              |====================================================================  |  97%  |                                                                              |====================================================================  |  98%  |                                                                              |===================================================================== |  98%  |                                                                              |===================================================================== |  99%  |                                                                              |======================================================================|  99%  |                                                                              |======================================================================| 100%

The following command line will output the mean error rate for each component and each tested keepX value given the past (tuned) components.

# Just a head of the classification error rate per keepX (in rows) and comp
head(tune.splsda.open.closed$error.rate)
##       comp1     comp2     comp3     comp4     comp5     comp6      comp7
## 1 0.3465901 0.2774625 0.2301887 0.1961860 0.1490299 0.1189066 0.10095682
## 2 0.3414441 0.2816839 0.2294705 0.1881141 0.1489022 0.1168132 0.09888667
## 3 0.3308625 0.2829726 0.2298002 0.1785037 0.1481507 0.1156044 0.09744034
## 4 0.3294250 0.2783594 0.2312288 0.1720069 0.1470785 0.1141103 0.09601177
## 5 0.3286469 0.2723443 0.2314308 0.1676701 0.1468232 0.1147075 0.09552781
## 6 0.3288722 0.2669231 0.2318881 0.1646431 0.1469808 0.1141581 0.09593185
##        comp8
## 1 0.09633922
## 2 0.09500833
## 3 0.09370740
## 4 0.09355311
## 5 0.09351759
## 6 0.09278388

This output globally shows that the classification error rate continues to decrease after the second component in sparse PLS-DA, however if only discriminating between two categorical outcomes, 1 or 2 components should be kept to avoid overfitting.***

We display the mean classification error rate on each component, bearing in mind that each component is conditional on the previous components calculated with the optimal number of selected variables. The diamond in the figure below indicates the best keepX value to achieve the lowest error rate per component.

# To show the error bars across the repeats:
plot(tune.splsda.open.closed, sd = TRUE)
Tuning keepX for the sPLS-DA performed on the IMOS GBR-MGD MAGs (876 genomes, drep at 95% ANI). Each coloured line represents the balanced error rate (y-axis) per component across all tested keepX values (x-axis) with the standard deviation based on the repeated cross-validation folds. The diamond indicates the optimal keepX value on a particular component which achieves the lowest classification error rate as determined with a one-sided t−test. As sPLS-DA is an iterative algorithm, values represented for a given component (e.g. comp 1 to 2) include the optimal keepX value chosen for the previous component (comp 1).

Tuning keepX for the sPLS-DA performed on the IMOS GBR-MGD MAGs (876 genomes, drep at 95% ANI). Each coloured line represents the balanced error rate (y-axis) per component across all tested keepX values (x-axis) with the standard deviation based on the repeated cross-validation folds. The diamond indicates the optimal keepX value on a particular component which achieves the lowest classification error rate as determined with a one-sided t−test. As sPLS-DA is an iterative algorithm, values represented for a given component (e.g. comp 1 to 2) include the optimal keepX value chosen for the previous component (comp 1).

The tuning results depend on the tuning grid list.keepX, as well as the values chosen for folds and nrepeat. Therefore, we recommend assessing the performance of the final model, as well as examining the stability of the selected variables across the different folds, as detailed in the next section.

The figure above shows that the error rate decreases when more components are included in sPLS-DA. To obtain a more reliable estimation of the error rate, the number of repeats should be increased (between 50 to 100). This type of graph helps not only to choose the ‘optimal’ number of variables to select, but also to confirm the number of components ncomp. From the code below, we can assess that in fact, the addition of a fourth component does not improve the classification (no statistically significant improvement according to a one-sided t−test), hence we can choose ncomp = 3.

# The optimal number of components according to our one-sided t-tests
tune.splsda.open.closed$choice.ncomp$ncomp
## [1] 7
# The optimal keepX parameter according to minimal error rate
tune.splsda.open.closed$choice.keepX
## comp1 comp2 comp3 comp4 comp5 comp6 comp7 comp8 
##     5    30   150    20   150   140     5    30

Final sPLS-DA model and performance

Here is our final sPLS-DA model with the optimal number of components and features (keepX) obtained from our tuning step.

# Optimal number of components based on t-tests on the error rate
ncomp <- tune.splsda.open.closed$choice.ncomp$ncomp 
ncomp
## [1] 7
# Optimal number of variables to select
select.keepX <- tune.splsda.open.closed$choice.keepX[1:ncomp]  
select.keepX
## comp1 comp2 comp3 comp4 comp5 comp6 comp7 
##     5    30   150    20   150   140     5
final.splsda.open.closed <- mixOmics::splsda(X = MAGs,
                                   Y = metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing,
                                   ncomp = ncomp,
                                   keepX = select.keepX) 
# You can choose to skip the tuning step, and input your arbitrarily chosen parameters in the following code (simply specify your own ncomp and keepX values):

The performance of the model with the ncomp and keepX parameters is assessed with the perf() function. We use 4-fold validation (folds = 4), repeated 50 times (nrepeat = 50).

The classification error rates that are output include both the overall error rate, as well as the balanced error rate (BER) when the number of samples per group is not balanced - as is the case in this study.

perf.final.splsda.open.closed <- perf(final.splsda.open.closed,
                                      folds = 4,
                                      validation = "Mfold",
                                      progressBar = TRUE,
                                      nrepeat = 50)
# perf.splsda.srbct  # Lists the different outputs
perf.final.splsda.open.closed$error.rate
## $overall
##        max.dist centroids.dist mahalanobis.dist
## comp1 0.3285263      0.3223158        0.3223158
## comp2 0.2477895      0.2894737        0.2474737
## comp3 0.2310526      0.3173684        0.2292632
## comp4 0.1648421      0.2978947        0.1656842
## comp5 0.1371579      0.2710526        0.1364211
## comp6 0.1211579      0.2544211        0.1211579
## comp7 0.1169474      0.2652632        0.1173684
## 
## $BER
##        max.dist centroids.dist mahalanobis.dist
## comp1 0.3291853      0.3221778        0.3221778
## comp2 0.2482295      0.2900588        0.2474292
## comp3 0.2329948      0.3164891        0.2305939
## comp4 0.1670973      0.2974914        0.1677189
## comp5 0.1387379      0.2693185        0.1378621
## comp6 0.1217238      0.2530481        0.1216262
## comp7 0.1171950      0.2640737        0.1175014

We can also examine the error rate per class:

perf.final.splsda.open.closed$error.rate.class
## $max.dist
##       comp1     comp2     comp3     comp4     comp5     comp6     comp7
## C 0.3448352 0.2586813 0.2791209 0.2206593 0.1762637 0.1351648 0.1230769
## O 0.3135354 0.2377778 0.1868687 0.1135354 0.1012121 0.1082828 0.1113131
## 
## $centroids.dist
##       comp1     comp2     comp3     comp4     comp5     comp6     comp7
## C 0.3189011 0.3039560 0.2956044 0.2879121 0.2281319 0.2204396 0.2358242
## O 0.3254545 0.2761616 0.3373737 0.3070707 0.3105051 0.2856566 0.2923232
## 
## $mahalanobis.dist
##       comp1     comp2     comp3     comp4     comp5     comp6     comp7
## C 0.3189011 0.2463736 0.2621978 0.2160440 0.1720879 0.1327473 0.1206593
## O 0.3254545 0.2484848 0.1989899 0.1193939 0.1036364 0.1105051 0.1143434

These results can be compared with the performance of PLS-DA and show the benefits of variable selection to not only obtain a parsimonious model, but also to improve the classification error rate (overall and per class).

Variable selection and stability

During the repeated cross-validation process in perf() we can record how often the same variables are selected across the folds. This information is important to answer the question: How reproducible is my molecular signature when the training set is perturbed via cross-validation?

par(mfrow=c(1,2))
# For component 1
stable.comp1 <- perf.final.splsda.open.closed$features$stable$comp1
barplot(stable.comp1,
        xlab = 'variables selected across CV folds', 
        ylab = 'Stability frequency',
        main = 'Feature stability for comp = 1')

# For component 2
stable.comp2 <- perf.final.splsda.open.closed$features$stable$comp2
barplot(stable.comp2,
        xlab = 'variables selected across CV folds', 
        ylab = 'Stability frequency',
        main = 'Feature stability for comp = 2')
Stability of variable selection from the sPLS-DA on the IMOS GBR-MGD MAGs data (876 MAGs, drep at 95% ANI). We use a by-product from perf() to assess how often the same MAGs are selected for a given keepX value in the final sPLS-DA model. The barplot represents the frequency of selection across repeated CV folds for each selected gene for component 1 and 2. The MAGs are ranked according to decreasing frequency.

Stability of variable selection from the sPLS-DA on the IMOS GBR-MGD MAGs data (876 MAGs, drep at 95% ANI). We use a by-product from perf() to assess how often the same MAGs are selected for a given keepX value in the final sPLS-DA model. The barplot represents the frequency of selection across repeated CV folds for each selected gene for component 1 and 2. The MAGs are ranked according to decreasing frequency.

par(mfrow=c(1,1))

The function selectVar() outputs the variables (pMAGs) selected for a given component and their loading values (ranked in decreasing absolute value). We concatenate those results with the feature stability, as shown here for variables selected on component 1:

# First extract the name of selected var:
select.name <- selectVar(final.splsda.open.closed, comp = 1)$name

# Then extract the stability values from perf:
stability <- perf.final.splsda.open.closed$features$stable$comp1[select.name]

# Just the head of the stability of the selected var:
head(cbind(selectVar(final.splsda.open.closed, comp = 1)$value, stability))

Sample visualisation

# Per reef protection status
spls.da.open.closed <- plotIndiv(final.splsda.open.closed,
          comp = c(1,2),
          ind.names = FALSE,
          pch = as.factor(sample_data(pMAGs_95ANI_phyloseq_clr)$Sampling_trip),
          group = sample_data(pMAGs_95ANI_phyloseq_clr)$Open_or_Closed_to_fishing,
          ellipse = TRUE,
          legend=TRUE,
          col.per.group = c("seagreen3", # Closed to fishing
                            "steelblue4"), # open to fishing
          legend.title = 'Reef Protection Status',
#          star = TRUE,
          title = 'IMOS-MGD MAGs open/closed, sPLS-DA comp 1 - 2')
# Per trip
spls.da.open.closed.per.trip <- plotIndiv(final.splsda.open.closed,
          comp = c(1,2),
          ind.names = FALSE,
          pch = as.factor(sample_data(pMAGs_95ANI_phyloseq_clr)$Open_or_Closed_to_fishing),
          group = sample_data(pMAGs_95ANI_phyloseq_clr)$Sampling_trip,
          ellipse = TRUE,
          legend=TRUE,
          col.per.group =c("indianred", # Sampling trip 1
                "indianred4", # Sampling trip 2 
                "red3", # Sampling trip 3
                "slateblue"), # Sampling trip 4
          legend.title = 'AIMS-LTMP Sampling transect',
#          star = TRUE,
          title = 'IMOS-MGD MAGs open/closed, sPLS-DA comp 1 - 2')

Are these sPLS-DA sample plots different than the PLS-DA plot? They are showing similar patterns - while we do see some clustering between the zones based on selected features, we still see strong spatiotemporal effects as well.

Variable visualisation

We represent the pMAGs selected with sPLS-DA on the correlation circle plot. Here to increase interpretation, we specify the argument var.names as the first 10 characters of the gene names. We also reduce the size of the font with the argument cex.

plotVar(final.splsda.open.closed,
        comp = c(1,2), 
        var.names = list(MAGs.name.super.short),
        cex = 3)
Correlation circle plot representing the MAGs selected by sPLS-DA performed on the 876 IMOS GBR-MGD MAGs (drep at 95% ANI). MAG names are truncated, and we only show the MAGs selected by sPLS-DA in components 1 and 2. This graphic should be interpreted in conjunction with the sample plot.

Correlation circle plot representing the MAGs selected by sPLS-DA performed on the 876 IMOS GBR-MGD MAGs (drep at 95% ANI). MAG names are truncated, and we only show the MAGs selected by sPLS-DA in components 1 and 2. This graphic should be interpreted in conjunction with the sample plot.

By considering both the correlation circle plot and the sample plot, we observe that a group of pMAGs with a positive correlation with component 1 (‘EH domain’, ‘proteasome’ etc.) are associated with the BL samples. We also observe two groups of genes either positively or negatively correlated with component 2. These genes are likely to characterise either the NB + RMS classes, or the EWS class.

This interpretation can be further examined with the plotLoadings() function. In this plot, the loading weights of each selected variable on each component are represented. The colours indicate the group in which the expression of the selected pMAGs is maximal based on the mean (method = ‘median’ is also available for skewed data). For example on component 1:

plotLoadings(final.splsda.open.closed,
             comp = 1,
             method = 'mean',
             contrib = 'max', 
             name.var = MAGs.name.super.short)
Loading plot of the MAGs selected by sPLS-DA on component 1 on the 876 IMOS GBR-MGD MAGs. MAGs are ranked according to their loading weight (most important at the bottom to least important at the top), represented as a barplot. Colours indicate the class for which a particular MAGs is maximally enriched, on average, in this particular class (i.e. no-take or take reefs). The plot helps to further characterise the molecular signatures and should be interpreted jointly with the sPLS-DA sample plot.

Loading plot of the MAGs selected by sPLS-DA on component 1 on the 876 IMOS GBR-MGD MAGs. MAGs are ranked according to their loading weight (most important at the bottom to least important at the top), represented as a barplot. Colours indicate the class for which a particular MAGs is maximally enriched, on average, in this particular class (i.e. no-take or take reefs). The plot helps to further characterise the molecular signatures and should be interpreted jointly with the sPLS-DA sample plot.

To complete the visualisation, the CIM in this special case is a simple hierarchical heatmap representing abundance values of the MAGs selected across all components with respect to each sample. Here we use an Euclidean distance with Complete agglomeration method, and we specify the argument row.sideColors to colour the samples according to their sampling trip.

cols.LTMP.trips <- c("indianred", # Sampling trip 1
                "indianred4", # Sampling trip 2 
                "red3", # Sampling trip 3
                "slateblue") # Sampling trip 4
LTMP.trips.cols <- palette(cols.LTMP.trips)[as.numeric(as.factor(metadata_IMOS_MGD_MAGs$Sampling_trip))]

cols.LTMP.trips <- c("indianred", # Sampling trip 1
                "indianred4", # Sampling trip 2 
                "red3", # Sampling trip 3
                "slateblue") # Sampling trip 4
LTMP.trips.cols <- palette(cols.LTMP.trips)[as.numeric(as.factor(metadata_IMOS_MGD_MAGs$Sampling_trip))]

cim(final.splsda.open.closed,
    comp = 1:2,
#    cutoff = 0.95,
    col.names = MAGs.name.short,
    margins=c(37, # bottom
              25), # right
    keysize = c(1, 0.4),
#    row.sideColors = color.mixo(as.numeric(as.factor(metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing))),
    row.names = T,
legend = list(color.mixo(as.numeric(as.factor(metadata_IMOS_MGD_MAGs$Sampling_trip))),
              title = "AIMS LTMP trips"),
    row.sideColors = LTMP.trips.cols,
    title = "sPLS-DA, components 1 and 2",
xlab = "Indicator MAGs that discriminate between take and no take zones",
ylab = "Reef sites")
Clustered Image Map of the MAGs selected by sPLS-DA on the 876 IMOS GBR-MGD MAGs on the first 2 components. A hierarchical clustering based on the MAG enrichment vales for the selected MAGs, with reef sites in rows coloured according to their reef protection status (and clustered using Euclidean distance with Complete agglomeration method).

Clustered Image Map of the MAGs selected by sPLS-DA on the 876 IMOS GBR-MGD MAGs on the first 2 components. A hierarchical clustering based on the MAG enrichment vales for the selected MAGs, with reef sites in rows coloured according to their reef protection status (and clustered using Euclidean distance with Complete agglomeration method).

cols.open.closed <- c("seagreen3","steelblue4")
open.closed.cols <- palette(cols.open.closed)[as.numeric(as.factor(metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing))]

cols.open.closed <- c("seagreen3","steelblue4")
open.closed.cols <- palette(cols.open.closed)[as.numeric(as.factor(metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing))]

cim(final.splsda.open.closed,
    comp = 1:2,
#    cutoff = 0.95,
    col.names = MAGs.name.short,
    margins=c(37, # bottom
              25), # right
    keysize = c(1, 0.4),
#    row.sideColors = color.mixo(as.numeric(as.factor(metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing))),
    row.names = T,
legend = list(color.mixo(as.numeric(as.factor(metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing))),
              title = "Reef Protection Status"),
    row.sideColors = open.closed.cols,
    title = "sPLS-DA, components 1 and 2",
xlab = "Indicator MAGs that discriminate between take and no take zones",
ylab = "Reef sites")
Clustered Image Map of the MAGs selected by sPLS-DA on the 876 IMOS GBR-MGD MAGs on the first 2 components. A hierarchical clustering based on the MAG enrichment vales for the selected MAGs, with reef sites in rows coloured according to their reef protection status (and clustered using Euclidean distance with Complete agglomeration method).

Clustered Image Map of the MAGs selected by sPLS-DA on the 876 IMOS GBR-MGD MAGs on the first 2 components. A hierarchical clustering based on the MAG enrichment vales for the selected MAGs, with reef sites in rows coloured according to their reef protection status (and clustered using Euclidean distance with Complete agglomeration method).

Overall, the (s)PLS-DA model is clearly selecting for winter-specific taxa, and we still see strong batch effects of seasonality and to a lesser extent geography. For monitoring purposes, it would be of higher utility to identify seawater biomarkers that would be stable indicators of reef zoning across the Great Barrier Reef, and regardless of season and geography.

In Terzin et al. 2025 (Microbiome) we used Multivariate INTegration (Rohart et al. 2017) to identify shared microbial indicators across the four sampling trips in our data, however, this study will also contain AIMS-LTMP benthic cover metrics, and since LTMP data has historically been analysed across GBR sectors, here we will select SECTOR as separate studies in MINT.

Let’s mine for stable microbial biomarkers.

MINT sPLS-DA with 876 IMOS-MGD MAGs (95% ANI) - discriminating between reefs that are open or closed to fishing (in sPLS-DA), while accounting for the sector-specific variability (MINT)

Tuning the number of dimensions

The perf() function is used to estimate the performance of the MINT-sPLS-DA model using Leave One Group Out Cross Validation (LOGOCV), and to choose the optimal number of components for our final model

# Extracting the dataframe
### Important: pMAGs_95ANI_phyloseq_CLR_per_sector is the new object where I clr transformed within each sector separately! The object MAGs should be made from this object: pMAGs_95ANI_phyloseq_clr, and it should be used when not accounting for sector (PCA, sPLS-DA, etc)
MAGs_MINT <- as.data.frame(pMAGs_95ANI_phyloseq_CLR_per_sector@otu_table)
MAGs_MINT <- t(MAGs_MINT)
# Check dimensions of data
dim(MAGs_MINT)
## [1] 190 876
class(MAGs_MINT)
## [1] "matrix" "array"
# This was already done in the code above - CLR normalised across all data
# MAGs <- as.data.frame(pMAGs_95ANI_phyloseq_clr@otu_table)
# MAGs <- t(MAGs)
# Check dimensions of data
# dim(MAGs)
# class(MAGs)

mint.splsda.open.closed <- mint.splsda(X = MAGs_MINT,
                              Y = pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Open_or_Closed_to_fishing,
                              study = pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Sampling_trip,
                              ncomp = 10)
perf.mint.splsda.open.closed <- perf(mint.splsda.open.closed)
plot(perf.mint.splsda.open.closed)
Choosing the number of components in mint.splsda using perf() with LOGOCV to discriminate between reefs that are open or closed to fishing. Classification error rates (overall and balanced - BER) are represented on the y-axis with respect to the number of components on the x-axis for each prediction distance. Overall and balanced error rates show the same trend as the design is balanced (i.e. the same number of protected and non-protected reefs in each sampling trip). The plot shows that the error rate reaches a minimum with three dimensions with the centroids prediction distance. We therefore retained 3 PCs in downstream analysis.

Choosing the number of components in mint.splsda using perf() with LOGOCV to discriminate between reefs that are open or closed to fishing. Classification error rates (overall and balanced - BER) are represented on the y-axis with respect to the number of components on the x-axis for each prediction distance. Overall and balanced error rates show the same trend as the design is balanced (i.e. the same number of protected and non-protected reefs in each sampling trip). The plot shows that the error rate reaches a minimum with three dimensions with the centroids prediction distance. We therefore retained 3 PCs in downstream analysis.

# Re-running MINT sPLS-DA
mint.splsda.open.closed.sector <- mint.splsda(X = MAGs_MINT,
                              Y = pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Open_or_Closed_to_fishing,
                              study = pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$SECTOR_N_S,
                              ncomp = 10)
perf.mint.splsda.open.closed.sector <- perf(mint.splsda.open.closed.sector)
plot(perf.mint.splsda.open.closed.sector)
Choosing the number of components in mint.splsda using perf() with LOGOCV to discriminate between reefs that are open or closed to fishing. Classification error rates (overall and balanced - BER) are represented on the y-axis with respect to the number of components on the x-axis for each prediction distance. Overall and balanced error rates show the same trend as the design is balanced (i.e. the same number of protected and non-protected reefs in each sampling trip). The plot shows that the error rate reaches a minimum with three dimensions with the centroids prediction distance. We therefore retained 3 PCs in downstream analysis.

Choosing the number of components in mint.splsda using perf() with LOGOCV to discriminate between reefs that are open or closed to fishing. Classification error rates (overall and balanced - BER) are represented on the y-axis with respect to the number of components on the x-axis for each prediction distance. Overall and balanced error rates show the same trend as the design is balanced (i.e. the same number of protected and non-protected reefs in each sampling trip). The plot shows that the error rate reaches a minimum with three dimensions with the centroids prediction distance. We therefore retained 3 PCs in downstream analysis.

# Filtering out the samples from Swains - this will be the query
pMAGs_95ANI_phyloseq_no_Swains <- subset_samples(pMAGs_95ANI_phyloseq, SECTOR_N_S != "06_Swains")
pMAGs_95ANI_phyloseq_Swains_only <- subset_samples(pMAGs_95ANI_phyloseq, SECTOR_N_S == "06_Swains")

# Need to CLR transform again - within each sector:
# 1. Extract sample data and sectors
sector_info <- sample_data(pMAGs_95ANI_phyloseq_no_Swains)$SECTOR_N_S
sectors <- unique(sector_info)

# 2. Initialize an empty list to store CLR-transformed subsets
phy_clr_list <- list()

# 3. Loop through each sector, apply CLR, and store results
for (sector in sectors) {
  # Subset phyloseq by sector
  phy_subset <- subset_samples(pMAGs_95ANI_phyloseq_no_Swains, SECTOR_N_S == sector)
  
  # Apply CLR to the subset (with pseudo-count to avoid zeros)
  phy_subset_clr <- microbiome::transform(phy_subset, transform = "clr")
  
  # Store in list
  phy_clr_list[[sector]] <- phy_subset_clr
}

# 4. Merge all sectors back into one phyloseq object
pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains <- do.call(merge_phyloseq, phy_clr_list)

# 5. Verify the output
head(otu_table(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains))  # Should show CLR values
## OTU Table:          [6 taxa and 170 samples]
##                      taxa are rows
##                          11049_1__BBG5542_21S000057 11049_2__BBG5543_21S000444
## 11049_1__concoct_009                       3.370796                  2.9741482
## 11049_1__concoct_027_sub                   3.123710                  3.1817013
## 11049_1__concoct_068                       5.768237                  5.3120043
## 11049_1__concoct_084                       1.684442                  0.9877569
## 11049_1__concoct_129_sub                   2.463162                  2.2821420
## 11049_1__concoct_161_sub                   2.222484                  2.0688801
##                          11049_3__BBG5544_21S000445 11049_4__BBG5545_21S000446
## 11049_1__concoct_009                      3.2916897                   3.252276
## 11049_1__concoct_027_sub                  2.9725147                   2.818456
## 11049_1__concoct_068                      5.4217023                   5.678063
## 11049_1__concoct_084                      0.9842408                   1.064172
## 11049_1__concoct_129_sub                  2.4067804                   2.416136
## 11049_1__concoct_161_sub                  2.3021121                   2.304723
##                          11162_1__BBG5534 11162_2__BBG5535 11162_3__BBG5536
## 11049_1__concoct_009            2.0948240         2.199595        2.3759332
## 11049_1__concoct_027_sub        1.8279075         2.634036        2.6258766
## 11049_1__concoct_068            4.9349705         5.612005        5.5430439
## 11049_1__concoct_084            0.8662672         1.296417        0.9540593
## 11049_1__concoct_129_sub        1.8090950         1.022383        1.2873464
## 11049_1__concoct_161_sub        2.4930078         2.170096        2.2373637
##                          11162_4__BBG5537 lagoon_1__BBG5466_21S000059
## 11049_1__concoct_009            2.3110268                  -3.5442912
## 11049_1__concoct_027_sub        3.9519461                   6.1133213
## 11049_1__concoct_068            5.1225528                   2.3098565
## 11049_1__concoct_084            0.3635965                  -3.0732106
## 11049_1__concoct_129_sub        1.2039118                  -5.1711209
## 11049_1__concoct_161_sub        1.9742170                  -0.1809867
##                          lagoon_2__BBG5467_21S000391
## 11049_1__concoct_009                       -4.406179
## 11049_1__concoct_027_sub                    4.846936
## 11049_1__concoct_068                        1.478775
## 11049_1__concoct_084                       -3.822232
## 11049_1__concoct_129_sub                   -3.766142
## 11049_1__concoct_161_sub                    0.275313
##                          lagoon_3__BBG5468_21S000392
## 11049_1__concoct_009                      -3.5364269
## 11049_1__concoct_027_sub                   6.5720419
## 11049_1__concoct_068                       2.1125473
## 11049_1__concoct_084                      -2.8533301
## 11049_1__concoct_129_sub                  -6.3498376
## 11049_1__concoct_161_sub                   0.0257549
##                          lagoon_4__BBG5469_21S000393
## 11049_1__concoct_009                      -4.2904015
## 11049_1__concoct_027_sub                   4.8503565
## 11049_1__concoct_068                       0.8802177
## 11049_1__concoct_084                      -4.7699746
## 11049_1__concoct_129_sub                  -3.8085635
## 11049_1__concoct_161_sub                  -0.2460979
##                          mantis_1__BBG5538_22S000873
## 11049_1__concoct_009                     -5.52400965
## 11049_1__concoct_027_sub                  5.01221404
## 11049_1__concoct_068                      1.43747595
## 11049_1__concoct_084                     -3.78354347
## 11049_1__concoct_129_sub                 -3.29399525
## 11049_1__concoct_161_sub                 -0.05342106
##                          mantis_2__BBG5539_21S000058
## 11049_1__concoct_009                      -5.7508481
## 11049_1__concoct_027_sub                   0.8089162
## 11049_1__concoct_068                       0.9059009
## 11049_1__concoct_084                      -3.1193380
## 11049_1__concoct_129_sub                  -2.9437732
## 11049_1__concoct_161_sub                   0.2863107
##                          mantis_3__BBG5540_21S000442
## 11049_1__concoct_009                      -4.2096440
## 11049_1__concoct_027_sub                   3.6598656
## 11049_1__concoct_068                       0.8771607
## 11049_1__concoct_084                      -3.4787565
## 11049_1__concoct_129_sub                  -3.1458178
## 11049_1__concoct_161_sub                   0.1559014
##                          mantis_4__BBG5541_21S000443
## 11049_1__concoct_009                      -5.8888147
## 11049_1__concoct_027_sub                   3.4022758
## 11049_1__concoct_068                       0.8568137
## 11049_1__concoct_084                      -3.0171351
## 11049_1__concoct_129_sub                  -3.6552225
## 11049_1__concoct_161_sub                   0.3937635
##                          mcSweeney_1__BBG5458_22S000870
## 11049_1__concoct_009                         -0.5025488
## 11049_1__concoct_027_sub                      4.4002476
## 11049_1__concoct_068                          4.2114713
## 11049_1__concoct_084                          0.9062853
## 11049_1__concoct_129_sub                      2.2057352
## 11049_1__concoct_161_sub                      0.8842465
##                          mcSweeney_2__BBG5459_21S000386
## 11049_1__concoct_009                         -0.1938102
## 11049_1__concoct_027_sub                      4.4438928
## 11049_1__concoct_068                          3.9745406
## 11049_1__concoct_084                          0.7396885
## 11049_1__concoct_129_sub                      2.3522330
## 11049_1__concoct_161_sub                      0.8081281
##                          mcSweeney_3__BBG5460_21S000055
## 11049_1__concoct_009                         -0.7558493
## 11049_1__concoct_027_sub                      3.1891906
## 11049_1__concoct_068                          3.7228825
## 11049_1__concoct_084                         -0.3236009
## 11049_1__concoct_129_sub                      2.3669472
## 11049_1__concoct_161_sub                      1.2721264
##                          mcSweeney_4__BBG5461_21S000387
## 11049_1__concoct_009                         -0.4222790
## 11049_1__concoct_027_sub                      3.5835740
## 11049_1__concoct_068                          3.6944218
## 11049_1__concoct_084                          0.6802937
## 11049_1__concoct_129_sub                      2.1370584
## 11049_1__concoct_161_sub                      0.9360145
##                          monsoon_1__BBG5474_21S000397
## 11049_1__concoct_009                        0.6553794
## 11049_1__concoct_027_sub                    3.8759839
## 11049_1__concoct_068                        3.6787005
## 11049_1__concoct_084                        0.6668389
## 11049_1__concoct_129_sub                    2.6310975
## 11049_1__concoct_161_sub                    1.0406188
##                          monsoon_2__BBG5475_21S000056
## 11049_1__concoct_009                        0.8558594
## 11049_1__concoct_027_sub                    5.3469434
## 11049_1__concoct_068                        5.0717512
## 11049_1__concoct_084                        2.1569714
## 11049_1__concoct_129_sub                    1.9529711
## 11049_1__concoct_161_sub                    1.0768312
##                          monsoon_3__BBG5476_22S000871
## 11049_1__concoct_009                        0.8035741
## 11049_1__concoct_027_sub                    4.5382756
## 11049_1__concoct_068                        4.5045801
## 11049_1__concoct_084                        1.5818124
## 11049_1__concoct_129_sub                    1.9975626
## 11049_1__concoct_161_sub                    1.3743526
##                          monsoon_4__BBG5477_21S000399
## 11049_1__concoct_009                        0.2039197
## 11049_1__concoct_027_sub                    5.4841818
## 11049_1__concoct_068                        5.1036234
## 11049_1__concoct_084                        2.4638963
## 11049_1__concoct_129_sub                    1.7036180
## 11049_1__concoct_161_sub                    1.1995614
##                          13124_1__BBG5462_21S000388 13124_2__BBG5463_21S000389
## 11049_1__concoct_009                     -0.8553297                 -0.6419458
## 11049_1__concoct_027_sub                  3.4578523                  4.1975302
## 11049_1__concoct_068                      1.8138944                  1.6527494
## 11049_1__concoct_084                     -3.3697122                 -4.4382373
## 11049_1__concoct_129_sub                 -2.3419259                 -2.1249949
## 11049_1__concoct_161_sub                  3.8163157                  3.6088799
##                          13124_3__BBG5464_21S000390 13124_4__BBG5465_21S000061
## 11049_1__concoct_009                      -1.272874                 -0.7874982
## 11049_1__concoct_027_sub                   3.292365                  2.9948523
## 11049_1__concoct_068                       1.274238                  1.6702823
## 11049_1__concoct_084                      -3.525390                 -4.8264927
## 11049_1__concoct_129_sub                  -2.419055                 -2.1184425
## 11049_1__concoct_161_sub                   3.490427                  3.7913670
##                          corbett_1__BBG5470_21S000394
## 11049_1__concoct_009                        2.1624164
## 11049_1__concoct_027_sub                    2.2965739
## 11049_1__concoct_068                       -0.2355982
## 11049_1__concoct_084                       -5.6186178
## 11049_1__concoct_129_sub                   -3.7860363
## 11049_1__concoct_161_sub                    2.9064231
##                          corbett_2__BBG5471_21S000395
## 11049_1__concoct_009                        2.2068148
## 11049_1__concoct_027_sub                    2.1214228
## 11049_1__concoct_068                       -0.2265411
## 11049_1__concoct_084                       -5.6662753
## 11049_1__concoct_129_sub                   -3.8055230
## 11049_1__concoct_161_sub                    2.8860276
##                          corbett_3__BBG5472_21S000396
## 11049_1__concoct_009                        2.2700011
## 11049_1__concoct_027_sub                    2.1061281
## 11049_1__concoct_068                       -0.2227685
## 11049_1__concoct_084                       -5.8566648
## 11049_1__concoct_129_sub                   -3.6410911
## 11049_1__concoct_161_sub                    2.9469096
##                          corbett_4__BBG5473_21S000060
## 11049_1__concoct_009                        2.3165793
## 11049_1__concoct_027_sub                    2.1206636
## 11049_1__concoct_068                       -0.1849683
## 11049_1__concoct_084                       -5.8678317
## 11049_1__concoct_129_sub                   -3.4827777
## 11049_1__concoct_161_sub                    2.9461467
##                          davie_1__BBG5454_21S000054 davie_3__BBG5456_21S000383
## 11049_1__concoct_009                       3.062380                  2.4210898
## 11049_1__concoct_027_sub                   2.974682                  1.4449672
## 11049_1__concoct_068                       1.511398                  0.8619122
## 11049_1__concoct_084                      -4.664010                 -3.5945795
## 11049_1__concoct_129_sub                  -4.307335                 -3.9623042
## 11049_1__concoct_161_sub                   1.655590                  1.9420277
##                          davie_4__BBG5457_22S000869
## 11049_1__concoct_009                      2.2778041
## 11049_1__concoct_027_sub                  1.6710214
## 11049_1__concoct_068                      0.5893236
## 11049_1__concoct_084                     -5.1648350
## 11049_1__concoct_129_sub                 -4.6052193
## 11049_1__concoct_161_sub                  1.8531190
##                          sanbank1_1__BBG5530_21S000062
## 11049_1__concoct_009                        -3.2599449
## 11049_1__concoct_027_sub                     3.5794350
## 11049_1__concoct_068                        -0.6069338
## 11049_1__concoct_084                        -4.3667877
## 11049_1__concoct_129_sub                    -5.8667413
## 11049_1__concoct_161_sub                     2.7936924
##                          sanbank1_2__BBG5531_21S000438
## 11049_1__concoct_009                        -2.6991173
## 11049_1__concoct_027_sub                     2.9349611
## 11049_1__concoct_068                        -0.7004593
## 11049_1__concoct_084                        -3.7202421
## 11049_1__concoct_129_sub                    -6.1050653
## 11049_1__concoct_161_sub                     2.7806326
##                          sanbank1_3__BBG5532_21S000439
## 11049_1__concoct_009                         -3.248642
## 11049_1__concoct_027_sub                      4.180362
## 11049_1__concoct_068                         -1.041467
## 11049_1__concoct_084                         -5.713746
## 11049_1__concoct_129_sub                     -6.601049
## 11049_1__concoct_161_sub                      2.363171
##                          sanbank1_4__BBG5533_21S000440
## 11049_1__concoct_009                         -2.906135
## 11049_1__concoct_027_sub                      2.621534
## 11049_1__concoct_068                         -1.151125
## 11049_1__concoct_084                         -4.113550
## 11049_1__concoct_129_sub                     -6.382233
## 11049_1__concoct_161_sub                      2.808380
##                          agincourt1_1__BBG6450_21S000073
## 11049_1__concoct_009                         -3.76319583
## 11049_1__concoct_027_sub                      3.16728347
## 11049_1__concoct_068                         -2.29054959
## 11049_1__concoct_084                         -5.64773703
## 11049_1__concoct_129_sub                     -4.78273959
## 11049_1__concoct_161_sub                     -0.05776113
##                          agincourt1_2__BBG6451_21S000475
## 11049_1__concoct_009                          -3.4128917
## 11049_1__concoct_027_sub                       3.9607882
## 11049_1__concoct_068                          -1.8140359
## 11049_1__concoct_084                          -5.1786757
## 11049_1__concoct_129_sub                      -5.3457298
## 11049_1__concoct_161_sub                      -0.1146211
##                          agincourt1_3__BBG6452_22S000879
## 11049_1__concoct_009                          -2.9224450
## 11049_1__concoct_027_sub                       4.4832338
## 11049_1__concoct_068                          -0.7267437
## 11049_1__concoct_084                          -5.1334629
## 11049_1__concoct_129_sub                      -5.0156799
## 11049_1__concoct_161_sub                      -0.5370812
##                          agincourt1_4__BBG6453_21S000477
## 11049_1__concoct_009                          -2.6300972
## 11049_1__concoct_027_sub                       4.5511359
## 11049_1__concoct_068                          -1.2382005
## 11049_1__concoct_084                          -4.6338269
## 11049_1__concoct_129_sub                      -7.1187335
## 11049_1__concoct_161_sub                      -0.4517767
##                          arlington_1__BBG6454_21S000478
## 11049_1__concoct_009                         -2.3748778
## 11049_1__concoct_027_sub                      2.6364086
## 11049_1__concoct_068                         -3.9196165
## 11049_1__concoct_084                         -4.6495776
## 11049_1__concoct_129_sub                     -4.4066315
## 11049_1__concoct_161_sub                      0.1040125
##                          arlington_2__BBG6455_21S000479
## 11049_1__concoct_009                          -1.232015
## 11049_1__concoct_027_sub                       3.702501
## 11049_1__concoct_068                          -3.109717
## 11049_1__concoct_084                          -2.950087
## 11049_1__concoct_129_sub                      -4.170589
## 11049_1__concoct_161_sub                       1.376973
##                          arlington_3__BBG6456_21S000480
## 11049_1__concoct_009                         -0.7379217
## 11049_1__concoct_027_sub                      4.3564217
## 11049_1__concoct_068                         -2.6253564
## 11049_1__concoct_084                         -2.5443873
## 11049_1__concoct_129_sub                     -4.0484647
## 11049_1__concoct_161_sub                      1.2764946
##                          arlington_4__BBG6457_21S000074
## 11049_1__concoct_009                         -0.2159744
## 11049_1__concoct_027_sub                      3.7511182
## 11049_1__concoct_068                         -2.9930175
## 11049_1__concoct_084                         -2.8096143
## 11049_1__concoct_129_sub                     -4.0317694
## 11049_1__concoct_161_sub                      1.5065035
##                          hastings_1__BBG6458_21S000481
## 11049_1__concoct_009                        -2.2026675
## 11049_1__concoct_027_sub                     3.8696712
## 11049_1__concoct_068                        -2.9737762
## 11049_1__concoct_084                        -6.5846941
## 11049_1__concoct_129_sub                    -4.8799460
## 11049_1__concoct_161_sub                     0.8592621
##                          hastings_2__BBG6459_21S000482
## 11049_1__concoct_009                        -2.5809328
## 11049_1__concoct_027_sub                     3.1820978
## 11049_1__concoct_068                        -3.0296266
## 11049_1__concoct_084                        -6.5321765
## 11049_1__concoct_129_sub                    -4.5040283
## 11049_1__concoct_161_sub                     0.6807078
##                          hastings_3__BBG6460_21S000483
## 11049_1__concoct_009                         -1.919981
## 11049_1__concoct_027_sub                      4.036361
## 11049_1__concoct_068                         -2.691600
## 11049_1__concoct_084                         -6.295738
## 11049_1__concoct_129_sub                     -4.314737
## 11049_1__concoct_161_sub                      1.127382
##                          hastings_4__BBG6461_21S000484
## 11049_1__concoct_009                        -2.2666045
## 11049_1__concoct_027_sub                     3.6444670
## 11049_1__concoct_068                        -2.6793424
## 11049_1__concoct_084                        -5.8075638
## 11049_1__concoct_129_sub                    -4.8912731
## 11049_1__concoct_161_sub                     0.8060441
##                          stcrispin_1__BBG5526_21S000434
## 11049_1__concoct_009                         -5.7204513
## 11049_1__concoct_027_sub                      4.8210407
## 11049_1__concoct_068                         -1.0230058
## 11049_1__concoct_084                         -3.1054915
## 11049_1__concoct_129_sub                     -4.7396220
## 11049_1__concoct_161_sub                     -0.1146492
##                          stcrispin_2__BBG5527_21S000435
## 11049_1__concoct_009                         -3.3731208
## 11049_1__concoct_027_sub                      4.7691025
## 11049_1__concoct_068                         -1.5621035
## 11049_1__concoct_084                         -5.2702408
## 11049_1__concoct_129_sub                     -4.5770936
## 11049_1__concoct_161_sub                     -0.7128613
##                          stcrispin_3__BBG5528_21S000436
## 11049_1__concoct_009                        -5.55532077
## 11049_1__concoct_027_sub                     5.03001600
## 11049_1__concoct_068                        -0.92180611
## 11049_1__concoct_084                        -3.16885419
## 11049_1__concoct_129_sub                    -5.23686704
## 11049_1__concoct_161_sub                     0.03846081
##                          stcrispin_4__BBG5529_21S000437
## 11049_1__concoct_009                         -4.5066029
## 11049_1__concoct_027_sub                      4.6504229
## 11049_1__concoct_068                         -0.9512549
## 11049_1__concoct_084                         -3.1909262
## 11049_1__concoct_129_sub                     -4.2654409
## 11049_1__concoct_161_sub                      0.2183684
##                          thetford_1__BBG6446_21S000471
## 11049_1__concoct_009                        -0.4165723
## 11049_1__concoct_027_sub                     2.8490724
## 11049_1__concoct_068                        -2.7383273
## 11049_1__concoct_084                        -4.7860201
## 11049_1__concoct_129_sub                    -4.6682371
## 11049_1__concoct_161_sub                     0.6599087
##                          thetford_2__BBG6447_21S000472
## 11049_1__concoct_009                       -0.02590532
## 11049_1__concoct_027_sub                    3.99237478
## 11049_1__concoct_068                       -2.31955005
## 11049_1__concoct_084                       -3.60153156
## 11049_1__concoct_129_sub                   -4.62738450
## 11049_1__concoct_161_sub                    0.62681598
##                          thetford_3__BBG6448_21S000473
## 11049_1__concoct_009                       -0.01788948
## 11049_1__concoct_027_sub                    3.20788024
## 11049_1__concoct_068                       -2.20678068
## 11049_1__concoct_084                       -4.19507005
## 11049_1__concoct_129_sub                   -4.69584534
## 11049_1__concoct_161_sub                    0.86675752
##                          thetford_4__BBG6449_22S000878 boult_1__BBG5478
## 11049_1__concoct_009                        -0.2763152       -3.1788441
## 11049_1__concoct_027_sub                     3.8317119        1.3510636
## 11049_1__concoct_068                        -2.5162166       -0.2830857
## 11049_1__concoct_084                        -3.8098895       -3.5236846
## 11049_1__concoct_129_sub                    -4.2466071       -4.8905609
## 11049_1__concoct_161_sub                     0.3448987        1.6900782
##                          boult_2__BBG5479 boult_3__BBG5480 boult_4__BBG5481
## 11049_1__concoct_009            -3.552563        -2.512553        -1.862364
## 11049_1__concoct_027_sub         3.651171         1.108121         3.390653
## 11049_1__concoct_068             1.641475         0.150035         1.492790
## 11049_1__concoct_084            -2.112544        -2.918018        -2.195264
## 11049_1__concoct_129_sub        -4.951930        -6.444378        -4.559943
## 11049_1__concoct_161_sub         1.467722         1.896793         1.722616
##                          broomfield_1__BBG5502_21S000066
## 11049_1__concoct_009                          -5.0595544
## 11049_1__concoct_027_sub                       3.3208060
## 11049_1__concoct_068                           2.9430200
## 11049_1__concoct_084                          -0.5370951
## 11049_1__concoct_129_sub                      -4.3007120
## 11049_1__concoct_161_sub                       2.7566386
##                          broomfield_2__BBG5503_22S000872
## 11049_1__concoct_009                           -3.415576
## 11049_1__concoct_027_sub                        1.907434
## 11049_1__concoct_068                            1.355108
## 11049_1__concoct_084                           -2.904751
## 11049_1__concoct_129_sub                       -3.127894
## 11049_1__concoct_161_sub                        1.152238
##                          broomfield_3__BBG5504_21S000417
## 11049_1__concoct_009                           -6.261119
## 11049_1__concoct_027_sub                        1.421248
## 11049_1__concoct_068                            1.381165
## 11049_1__concoct_084                           -1.663477
## 11049_1__concoct_129_sub                       -4.469360
## 11049_1__concoct_161_sub                        2.303101
##                          broomfield_4__BBG5505_21S000418
## 11049_1__concoct_009                           -6.505017
## 11049_1__concoct_027_sub                        3.457517
## 11049_1__concoct_068                            2.464715
## 11049_1__concoct_084                           -0.257942
## 11049_1__concoct_129_sub                       -4.425576
## 11049_1__concoct_161_sub                        2.014573
##                          erskine_1__BBG5514_21S000425
## 11049_1__concoct_009                       -4.9509647
## 11049_1__concoct_027_sub                    0.0151869
## 11049_1__concoct_068                        2.9012288
## 11049_1__concoct_084                       -2.2822756
## 11049_1__concoct_129_sub                   -4.6373072
## 11049_1__concoct_161_sub                    2.1224388
##                          erskine_2__BBG5515_21S000426
## 11049_1__concoct_009                       -5.1354324
## 11049_1__concoct_027_sub                    0.2864844
## 11049_1__concoct_068                        2.9844870
## 11049_1__concoct_084                       -2.1028862
## 11049_1__concoct_129_sub                   -4.4740339
## 11049_1__concoct_161_sub                    2.0235192
##                          erskine_3__BBG5516_21S000427
## 11049_1__concoct_009                       -5.0847685
## 11049_1__concoct_027_sub                    0.2214587
## 11049_1__concoct_068                        2.8206298
## 11049_1__concoct_084                       -2.1280217
## 11049_1__concoct_129_sub                   -5.0847685
## 11049_1__concoct_161_sub                    2.2539285
##                          erskine_4__BBG5517_21S000065
## 11049_1__concoct_009                        -5.587851
## 11049_1__concoct_027_sub                     0.661363
## 11049_1__concoct_068                         3.105627
## 11049_1__concoct_084                        -2.372011
## 11049_1__concoct_129_sub                    -4.474201
## 11049_1__concoct_161_sub                     2.182570
##                          fairfax_1__BBG5486_21S000403
## 11049_1__concoct_009                       -2.4100176
## 11049_1__concoct_027_sub                    1.5585924
## 11049_1__concoct_068                        0.7295171
## 11049_1__concoct_084                       -3.6289465
## 11049_1__concoct_129_sub                   -5.3544565
## 11049_1__concoct_161_sub                    2.1215802
##                          fairfax_2__BBG5487_21S000404
## 11049_1__concoct_009                        -2.885069
## 11049_1__concoct_027_sub                     3.576362
## 11049_1__concoct_068                         1.253976
## 11049_1__concoct_084                        -2.959177
## 11049_1__concoct_129_sub                    -4.864881
## 11049_1__concoct_161_sub                     1.629238
##                          fairfax_3__BBG5488_21S000405
## 11049_1__concoct_009                        -2.586107
## 11049_1__concoct_027_sub                     4.040121
## 11049_1__concoct_068                         1.626064
## 11049_1__concoct_084                        -2.217937
## 11049_1__concoct_129_sub                    -4.372102
## 11049_1__concoct_161_sub                     1.447264
##                          fairfax_4__BBG5489_21S000406
## 11049_1__concoct_009                        -3.826443
## 11049_1__concoct_027_sub                     3.755048
## 11049_1__concoct_068                         0.801106
## 11049_1__concoct_084                        -2.810069
## 11049_1__concoct_129_sub                    -4.979123
## 11049_1__concoct_161_sub                     1.501560
##                          hoskyn_1__BBG5482_21S000400
## 11049_1__concoct_009                       -4.418132
## 11049_1__concoct_027_sub                    1.315816
## 11049_1__concoct_068                        1.244612
## 11049_1__concoct_084                       -2.241961
## 11049_1__concoct_129_sub                   -5.398961
## 11049_1__concoct_161_sub                    1.920517
##                          hoskyn_2__BBG5483_21S000063
## 11049_1__concoct_009                      -4.7476191
## 11049_1__concoct_027_sub                   0.9485714
## 11049_1__concoct_068                       1.3344266
## 11049_1__concoct_084                      -1.8229755
## 11049_1__concoct_129_sub                  -5.2134934
## 11049_1__concoct_161_sub                   2.2041728
##                          hoskyn_3__BBG5484_21S000401
## 11049_1__concoct_009                      -4.0232455
## 11049_1__concoct_027_sub                   3.8149736
## 11049_1__concoct_068                       2.3738693
## 11049_1__concoct_084                      -0.9432061
## 11049_1__concoct_129_sub                  -4.6800251
## 11049_1__concoct_161_sub                   1.6561684
##                          hoskyn_4__BBG5485_21S000402
## 11049_1__concoct_009                       -4.026879
## 11049_1__concoct_027_sub                    1.007002
## 11049_1__concoct_068                        1.239690
## 11049_1__concoct_084                       -2.277679
## 11049_1__concoct_129_sub                   -5.045449
## 11049_1__concoct_161_sub                    2.147948
##                          masthead_1__BBG5506_21S000419
## 11049_1__concoct_009                        -4.8317524
## 11049_1__concoct_027_sub                     0.3957847
## 11049_1__concoct_068                         2.5608130
## 11049_1__concoct_084                        -2.0103736
## 11049_1__concoct_129_sub                    -4.1058154
## 11049_1__concoct_161_sub                     1.4711107
##                          masthead_2__BBG5507_21S000420
## 11049_1__concoct_009                        -4.7625910
## 11049_1__concoct_027_sub                    -0.2604032
## 11049_1__concoct_068                         2.5994649
## 11049_1__concoct_084                        -2.2896605
## 11049_1__concoct_129_sub                    -4.2235945
## 11049_1__concoct_161_sub                     1.9720856
##                          masthead_3__BBG5508_21S000421
## 11049_1__concoct_009                        -4.3582787
## 11049_1__concoct_027_sub                    -0.1879129
## 11049_1__concoct_068                         2.5129028
## 11049_1__concoct_084                        -2.1756529
## 11049_1__concoct_129_sub                    -4.6034012
## 11049_1__concoct_161_sub                     2.0871650
##                          masthead_4__BBG5509_21S000064
## 11049_1__concoct_009                        -4.5814098
## 11049_1__concoct_027_sub                    -0.2741701
## 11049_1__concoct_068                         2.8736233
## 11049_1__concoct_084                        -1.8095567
## 11049_1__concoct_129_sub                    -4.4807663
## 11049_1__concoct_161_sub                     2.2832292
##                          north_1__BBG5490_21S000072 north_2__BBG5491_21S000407
## 11049_1__concoct_009                     -5.5166782                 -5.3877846
## 11049_1__concoct_027_sub                  0.8858729                  0.9932791
## 11049_1__concoct_068                      0.6831745                  0.8713718
## 11049_1__concoct_084                     -2.5941493                 -3.2283004
## 11049_1__concoct_129_sub                 -4.4180659                 -3.4578748
## 11049_1__concoct_161_sub                  2.6259242                  2.7265401
##                          north_3__BBG5492_21S000408 north_4__BBG5493_21S000409
## 11049_1__concoct_009                      -5.783156                 -5.4517141
## 11049_1__concoct_027_sub                   2.372042                  1.4374952
## 11049_1__concoct_068                       1.056779                  0.9470888
## 11049_1__concoct_084                      -2.002218                 -2.8677166
## 11049_1__concoct_129_sub                  -3.411578                 -4.1989512
## 11049_1__concoct_161_sub                   2.804656                  2.8216544
##                          centipede_1__BBG6474 centipede_2__BBG6475
## 11049_1__concoct_009               -6.9089596           -6.4552769
## 11049_1__concoct_027_sub            4.3917437            6.3870630
## 11049_1__concoct_068               -2.1008485           -0.6088381
## 11049_1__concoct_084               -4.0467587           -3.4595446
## 11049_1__concoct_129_sub           -3.6318148           -5.0689825
## 11049_1__concoct_161_sub           -0.9262835           -1.6349953
##                          centipede_3__BBG6476 centipede_4__BBG6477
## 11049_1__concoct_009                -7.507232           -6.8592760
## 11049_1__concoct_027_sub             5.657658            5.7964349
## 11049_1__concoct_068                -1.431120           -0.9621221
## 11049_1__concoct_084                -4.275111           -2.9880750
## 11049_1__concoct_129_sub            -4.416190           -4.0866873
## 11049_1__concoct_161_sub            -1.292624           -1.5265572
##                          chicken_1__BBG6486_22S000883
## 11049_1__concoct_009                        -6.408612
## 11049_1__concoct_027_sub                     3.897217
## 11049_1__concoct_068                        -3.324084
## 11049_1__concoct_084                        -4.260178
## 11049_1__concoct_129_sub                    -2.825093
## 11049_1__concoct_161_sub                    -1.792078
##                          chicken_2__BBG6487_22S000884
## 11049_1__concoct_009                        -5.408766
## 11049_1__concoct_027_sub                     5.866088
## 11049_1__concoct_068                        -1.996519
## 11049_1__concoct_084                        -3.249282
## 11049_1__concoct_129_sub                    -3.799328
## 11049_1__concoct_161_sub                    -2.317724
##                          chicken_3__BBG6488_21S000078
## 11049_1__concoct_009                        -5.997466
## 11049_1__concoct_027_sub                     4.663995
## 11049_1__concoct_068                        -2.884370
## 11049_1__concoct_084                        -3.869684
## 11049_1__concoct_129_sub                    -3.001734
## 11049_1__concoct_161_sub                    -1.583183
##                          chicken_4__BBG6489_21S000501
## 11049_1__concoct_009                        -5.614647
## 11049_1__concoct_027_sub                     3.735021
## 11049_1__concoct_068                        -3.157911
## 11049_1__concoct_084                        -4.444575
## 11049_1__concoct_129_sub                    -3.032748
## 11049_1__concoct_161_sub                    -1.644355
##                          foreAndAft_1__BBG6494_21S000506
## 11049_1__concoct_009                           -5.197126
## 11049_1__concoct_027_sub                        5.527847
## 11049_1__concoct_068                           -1.237818
## 11049_1__concoct_084                           -4.530647
## 11049_1__concoct_129_sub                       -3.967178
## 11049_1__concoct_161_sub                       -1.350344
##                          foreAndAft_2__BBG6495_21S000507
## 11049_1__concoct_009                           -5.047776
## 11049_1__concoct_027_sub                        5.701018
## 11049_1__concoct_068                           -1.155955
## 11049_1__concoct_084                           -4.865454
## 11049_1__concoct_129_sub                       -3.884625
## 11049_1__concoct_161_sub                       -1.066227
##                          foreAndAft_3__BBG6496_21S000508
## 11049_1__concoct_009                          -5.3712812
## 11049_1__concoct_027_sub                       4.7154766
## 11049_1__concoct_068                          -1.7307753
## 11049_1__concoct_084                          -4.5239833
## 11049_1__concoct_129_sub                      -3.9049441
## 11049_1__concoct_161_sub                      -0.8422724
##                          foreAndAft_4__BBG6497_21S000509
## 11049_1__concoct_009                          -5.3614746
## 11049_1__concoct_027_sub                       4.5877721
## 11049_1__concoct_068                          -1.8124959
## 11049_1__concoct_084                          -5.2561140
## 11049_1__concoct_129_sub                      -4.3806453
## 11049_1__concoct_161_sub                      -0.9547553
##                          fork_1__BBG6466_21S000489 fork_2__BBG6467_21S000490
## 11049_1__concoct_009                     -6.028429                 -6.260061
## 11049_1__concoct_027_sub                  3.347906                  3.233502
## 11049_1__concoct_068                     -3.498266                 -3.585912
## 11049_1__concoct_084                     -4.020961                 -3.908685
## 11049_1__concoct_129_sub                 -2.761822                 -3.001964
## 11049_1__concoct_161_sub                 -1.526154                 -1.458091
##                          fork_3__BBG6468_21S000491 fork_4__BBG6469_21S000492
## 11049_1__concoct_009                     -5.743402                 -6.056514
## 11049_1__concoct_027_sub                  3.314423                  3.375288
## 11049_1__concoct_068                     -3.619509                 -3.561245
## 11049_1__concoct_084                     -4.270096                 -4.307314
## 11049_1__concoct_129_sub                 -2.818287                 -2.878460
## 11049_1__concoct_161_sub                 -1.519892                 -1.457613
##                          grub_1__BBG6482_21S000496 grub_2__BBG6483_21S000497
## 11049_1__concoct_009                     -5.574611                 -5.899169
## 11049_1__concoct_027_sub                  3.860115                  3.299470
## 11049_1__concoct_068                     -3.162827                 -3.027489
## 11049_1__concoct_084                     -4.310919                 -4.289731
## 11049_1__concoct_129_sub                 -3.102608                 -3.018099
## 11049_1__concoct_161_sub                 -1.785191                 -1.638839
##                          grub_3__BBG6484_21S000079 grub_4__BBG6485_22S000882
## 11049_1__concoct_009                     -6.043031                 -6.444599
## 11049_1__concoct_027_sub                  3.429672                  3.708284
## 11049_1__concoct_068                     -3.069771                 -3.036757
## 11049_1__concoct_084                     -4.602669                 -4.365158
## 11049_1__concoct_129_sub                 -3.048688                 -2.812290
## 11049_1__concoct_161_sub                 -1.600706                 -1.680718
##                          helix_1__BBG6478 helix_2__BBG6479 helix_3__BBG6480
## 11049_1__concoct_009            -5.626461        -6.115163        -6.114589
## 11049_1__concoct_027_sub         3.024038         2.496567         4.037262
## 11049_1__concoct_068            -3.061512        -2.730773        -1.409573
## 11049_1__concoct_084            -4.710170        -3.787885        -2.296877
## 11049_1__concoct_129_sub        -2.448407        -1.984005        -2.875910
## 11049_1__concoct_161_sub        -1.414333        -1.003175        -1.451150
##                          helix_4__BBG6481 johnBrewer_1__BBG6510_21S000521
## 11049_1__concoct_009           -7.2886206                       -7.170177
## 11049_1__concoct_027_sub        2.4179240                        3.974492
## 11049_1__concoct_068           -3.0294681                       -1.476445
## 11049_1__concoct_084           -3.5873187                       -5.224267
## 11049_1__concoct_129_sub       -2.4134233                       -4.605228
## 11049_1__concoct_161_sub       -0.9741672                       -1.041127
##                          johnBrewer_2__BBG6511_21S000522
## 11049_1__concoct_009                          -6.3029365
## 11049_1__concoct_027_sub                       4.9153360
## 11049_1__concoct_068                          -0.7903145
## 11049_1__concoct_084                          -3.7227197
## 11049_1__concoct_129_sub                      -4.6542779
## 11049_1__concoct_161_sub                      -1.2227751
##                          johnBrewer_3__BBG6512_22S000887
## 11049_1__concoct_009                          -6.0067349
## 11049_1__concoct_027_sub                       4.1862549
## 11049_1__concoct_068                          -1.2171620
## 11049_1__concoct_084                          -4.0971924
## 11049_1__concoct_129_sub                      -4.8280799
## 11049_1__concoct_161_sub                      -0.7823332
##                          johnBrewer_4__BBG6513_21S000524
## 11049_1__concoct_009                          -6.9213761
## 11049_1__concoct_027_sub                       3.8369947
## 11049_1__concoct_068                          -1.5647899
## 11049_1__concoct_084                          -4.6187910
## 11049_1__concoct_129_sub                      -5.3119382
## 11049_1__concoct_161_sub                      -0.9274147
##                          kelso_1__BBG6502_21S000514 kelso_2__BBG6503_21S000515
## 11049_1__concoct_009                      -5.251685                  -5.352297
## 11049_1__concoct_027_sub                   4.884708                   4.536768
## 11049_1__concoct_068                      -1.717998                  -2.195297
## 11049_1__concoct_084                      -4.181243                  -4.716308
## 11049_1__concoct_129_sub                  -3.676148                  -3.617696
## 11049_1__concoct_161_sub                  -1.233801                  -1.170247
##                          kelso_3__BBG6504_21S000516 kelso_4__BBG6505_21S000076
## 11049_1__concoct_009                      -4.719254                  -5.346904
## 11049_1__concoct_027_sub                   4.712165                   5.149558
## 11049_1__concoct_068                      -2.037179                  -1.634959
## 11049_1__concoct_084                      -4.645146                  -4.521268
## 11049_1__concoct_129_sub                  -3.603692                  -3.927820
## 11049_1__concoct_161_sub                  -1.158062                  -1.158513
##                          knife_1__BBG6462_22S000880 knife_2__BBG6463_22S000881
## 11049_1__concoct_009                      -5.820239                  -5.313119
## 11049_1__concoct_027_sub                   3.449077                   3.420757
## 11049_1__concoct_068                      -3.367081                  -3.585898
## 11049_1__concoct_084                      -4.373320                  -4.115415
## 11049_1__concoct_129_sub                  -2.642185                  -2.892750
## 11049_1__concoct_161_sub                  -1.589763                  -1.581419
##                          knife_3__BBG6464_21S000487 knife_4__BBG6465_21S000488
## 11049_1__concoct_009                      -7.195504                  -7.279832
## 11049_1__concoct_027_sub                   3.710341                   3.499645
## 11049_1__concoct_068                      -3.345357                  -3.367809
## 11049_1__concoct_084                      -4.225090                  -4.640775
## 11049_1__concoct_129_sub                  -2.712502                  -3.045726
## 11049_1__concoct_161_sub                  -1.615775                  -1.442102
##                          littleKelso_1__BBG6498_22S000885
## 11049_1__concoct_009                            -6.297769
## 11049_1__concoct_027_sub                         5.297372
## 11049_1__concoct_068                            -1.042881
## 11049_1__concoct_084                            -4.218327
## 11049_1__concoct_129_sub                        -4.425967
## 11049_1__concoct_161_sub                        -1.531330
##                          littleKelso_2__BBG6499_21S000511
## 11049_1__concoct_009                            -5.008529
## 11049_1__concoct_027_sub                         5.205202
## 11049_1__concoct_068                            -1.296584
## 11049_1__concoct_084                            -4.720847
## 11049_1__concoct_129_sub                        -3.526924
## 11049_1__concoct_161_sub                        -1.035724
##                          littleKelso_3__BBG6500_21S000512
## 11049_1__concoct_009                            -4.836794
## 11049_1__concoct_027_sub                         4.733223
## 11049_1__concoct_068                            -1.499839
## 11049_1__concoct_084                            -4.325969
## 11049_1__concoct_129_sub                        -3.613019
## 11049_1__concoct_161_sub                        -1.034586
##                          littleKelso_4__BBG6501_22S000886
## 11049_1__concoct_009                           -4.9803174
## 11049_1__concoct_027_sub                        4.3959187
## 11049_1__concoct_068                           -1.7465529
## 11049_1__concoct_084                           -4.2265456
## 11049_1__concoct_129_sub                       -4.0312368
## 11049_1__concoct_161_sub                       -0.9321622
##                          lynchs_1__BBG6514_21S000525
## 11049_1__concoct_009                       -6.503589
## 11049_1__concoct_027_sub                    4.032791
## 11049_1__concoct_068                       -2.269483
## 11049_1__concoct_084                       -3.459067
## 11049_1__concoct_129_sub                   -4.424148
## 11049_1__concoct_161_sub                   -1.492954
##                          lynchs_2__BBG6515_22S000888
## 11049_1__concoct_009                       -6.199068
## 11049_1__concoct_027_sub                    5.037838
## 11049_1__concoct_068                       -1.905872
## 11049_1__concoct_084                       -3.748062
## 11049_1__concoct_129_sub                   -4.673011
## 11049_1__concoct_161_sub                   -1.515086
##                          lynchs_3__BBG6516_21S000527
## 11049_1__concoct_009                       -7.241817
## 11049_1__concoct_027_sub                    5.755158
## 11049_1__concoct_068                       -1.407006
## 11049_1__concoct_084                       -3.807830
## 11049_1__concoct_129_sub                   -5.450058
## 11049_1__concoct_161_sub                   -1.953550
##                          lynchs_4__BBG6517_21S000528
## 11049_1__concoct_009                       -6.141683
## 11049_1__concoct_027_sub                    4.278035
## 11049_1__concoct_068                       -2.014549
## 11049_1__concoct_084                       -3.944459
## 11049_1__concoct_129_sub                   -3.502626
## 11049_1__concoct_161_sub                   -1.405485
##                          myrmidon_1__BBG6470_21S000493
## 11049_1__concoct_009                        -6.2201597
## 11049_1__concoct_027_sub                    -0.8040593
## 11049_1__concoct_068                        -3.7352531
## 11049_1__concoct_084                        -3.8222645
## 11049_1__concoct_129_sub                    -1.8134405
## 11049_1__concoct_161_sub                    -0.9369560
##                          myrmidon_2__BBG6471_21S000494
## 11049_1__concoct_009                        -7.2302079
## 11049_1__concoct_027_sub                    -0.6128049
## 11049_1__concoct_068                        -3.9343710
## 11049_1__concoct_084                        -4.4576191
## 11049_1__concoct_129_sub                    -2.3175530
## 11049_1__concoct_161_sub                    -0.8382907
##                          myrmidon_3__BBG6472_21S000077
## 11049_1__concoct_009                        -7.1710099
## 11049_1__concoct_027_sub                    -0.5704594
## 11049_1__concoct_068                        -4.0140095
## 11049_1__concoct_084                        -4.0574946
## 11049_1__concoct_129_sub                    -1.9615238
## 11049_1__concoct_161_sub                    -0.8262511
##                          myrmidon_4__BBG6473_21S000495 rib_1__BBG6490_21S000502
## 11049_1__concoct_009                        -5.5566682               -5.3012243
## 11049_1__concoct_027_sub                    -0.3918822                5.0389545
## 11049_1__concoct_068                        -4.7093703               -0.8647301
## 11049_1__concoct_084                        -3.9472303               -4.4854748
## 11049_1__concoct_129_sub                    -1.8677888               -4.5865710
## 11049_1__concoct_161_sub                    -0.7553831               -0.6098765
##                          rib_2__BBG6491_21S000503 rib_3__BBG6492_21S000504
## 11049_1__concoct_009                   -4.8239016               -5.9172183
## 11049_1__concoct_027_sub                4.9450912                5.6382781
## 11049_1__concoct_068                   -0.9199108               -0.5327232
## 11049_1__concoct_084                   -5.3347272               -5.2240711
## 11049_1__concoct_129_sub               -4.6007581               -4.1944517
## 11049_1__concoct_161_sub               -0.7345696               -0.9336116
##                          rib_4__BBG6493_21S000505 roxburgh_1__BBG6506_21S000517
## 11049_1__concoct_009                   -4.5718556                     -4.702599
## 11049_1__concoct_027_sub                4.9865964                      5.143267
## 11049_1__concoct_068                   -1.0000538                     -1.225564
## 11049_1__concoct_084                   -4.5401069                     -4.849203
## 11049_1__concoct_129_sub               -4.1346418                     -3.901821
## 11049_1__concoct_161_sub               -0.6715135                     -1.109030
##                          roxburgh_2__BBG6507_21S000518
## 11049_1__concoct_009                         -4.883735
## 11049_1__concoct_027_sub                      5.027373
## 11049_1__concoct_068                         -1.363789
## 11049_1__concoct_084                         -4.761133
## 11049_1__concoct_129_sub                     -4.048938
## 11049_1__concoct_161_sub                     -1.132698
##                          roxburgh_3__BBG6508_21S000519
## 11049_1__concoct_009                         -4.962132
## 11049_1__concoct_027_sub                      4.116002
## 11049_1__concoct_068                         -1.389786
## 11049_1__concoct_084                         -4.045841
## 11049_1__concoct_129_sub                     -4.129223
## 11049_1__concoct_161_sub                     -1.082632
##                          roxburgh_4__BBG6509_21S000520
## 11049_1__concoct_009                         -5.016228
## 11049_1__concoct_027_sub                      5.257095
## 11049_1__concoct_068                         -1.029893
## 11049_1__concoct_084                         -4.099938
## 11049_1__concoct_129_sub                     -4.659553
## 11049_1__concoct_161_sub                     -1.178313
##                          farquaharson_1__BBG6418_21S000448
## 11049_1__concoct_009                            -1.5090073
## 11049_1__concoct_027_sub                         4.4148569
## 11049_1__concoct_068                            -1.6705518
## 11049_1__concoct_084                            -5.0027563
## 11049_1__concoct_129_sub                        -3.3752999
## 11049_1__concoct_161_sub                         0.6232284
##                          farquaharson_2__BBG6419_22S000874
## 11049_1__concoct_009                            -1.6930765
## 11049_1__concoct_027_sub                         4.1126189
## 11049_1__concoct_068                            -1.7361757
## 11049_1__concoct_084                            -4.2580259
## 11049_1__concoct_129_sub                        -2.8717315
## 11049_1__concoct_161_sub                         0.7986308
##                          farquaharson_3__BBG6420_21S000450
## 11049_1__concoct_009                            -1.4477020
## 11049_1__concoct_027_sub                         4.2177010
## 11049_1__concoct_068                            -1.2798816
## 11049_1__concoct_084                            -4.3215989
## 11049_1__concoct_129_sub                        -3.5438944
## 11049_1__concoct_161_sub                         0.4829041
##                          farquaharson_4__BBG6421_22S000875 feather_1__BBG6422
## 11049_1__concoct_009                            -1.6148564          0.3190216
## 11049_1__concoct_027_sub                         3.6138539          3.0635798
## 11049_1__concoct_068                            -1.5448125         -2.3377353
## 11049_1__concoct_084                            -4.8088088         -5.8492807
## 11049_1__concoct_129_sub                        -2.4611032         -4.3733742
## 11049_1__concoct_161_sub                         0.9522746          0.7504197
##                          feather_2__BBG6423 feather_3__BBG6424
## 11049_1__concoct_009              0.1213511         -0.6167127
## 11049_1__concoct_027_sub          3.1194361          2.7660431
## 11049_1__concoct_068             -2.6263217         -2.4006901
## 11049_1__concoct_084             -5.2412815         -5.0632779
## 11049_1__concoct_129_sub         -3.7319271         -3.7051544
## 11049_1__concoct_161_sub          0.8104715          0.9189777
##                          feather_4__BBG6425 hedley_1__BBG6438_21S000463
## 11049_1__concoct_009              0.1090817                    2.594059
## 11049_1__concoct_027_sub          2.6582062                    1.901518
## 11049_1__concoct_068             -2.7165903                   -1.911089
## 11049_1__concoct_084             -5.7879600                   -5.624661
## 11049_1__concoct_129_sub         -3.8275778                   -4.613060
## 11049_1__concoct_161_sub          0.7325409                    1.854639
##                          hedley_3__BBG6439_21S000464
## 11049_1__concoct_009                       2.8342211
## 11049_1__concoct_027_sub                   2.6742251
## 11049_1__concoct_068                      -2.1230465
## 11049_1__concoct_084                      -5.3920721
## 11049_1__concoct_129_sub                  -4.2777115
## 11049_1__concoct_161_sub                   0.5291232
##                          hedley_4__BBG6440_21S000465
## 11049_1__concoct_009                        2.373548
## 11049_1__concoct_027_sub                    2.694616
## 11049_1__concoct_068                       -1.899532
## 11049_1__concoct_084                       -5.375631
## 11049_1__concoct_129_sub                   -4.682483
## 11049_1__concoct_161_sub                    2.264706
##                          mcCulloch_1__BBG6434_21S000459
## 11049_1__concoct_009                           2.019779
## 11049_1__concoct_027_sub                       2.456426
## 11049_1__concoct_068                          -1.976125
## 11049_1__concoct_084                          -4.835725
## 11049_1__concoct_129_sub                      -4.098126
## 11049_1__concoct_161_sub                       2.504344
##                          mcCulloch_2__BBG6435_21S000460
## 11049_1__concoct_009                           2.163404
## 11049_1__concoct_027_sub                       3.036309
## 11049_1__concoct_068                          -2.100115
## 11049_1__concoct_084                          -5.161805
## 11049_1__concoct_129_sub                      -4.263864
## 11049_1__concoct_161_sub                       2.056771
##                          mcCulloch_3__BBG6436_21S000461
## 11049_1__concoct_009                           1.813805
## 11049_1__concoct_027_sub                       4.800722
## 11049_1__concoct_068                          -1.358892
## 11049_1__concoct_084                          -5.582070
## 11049_1__concoct_129_sub                      -4.077992
## 11049_1__concoct_161_sub                       1.390771
##                          mcCulloch_4__BBG6437_21S000462
## 11049_1__concoct_009                           2.291414
## 11049_1__concoct_027_sub                       2.689377
## 11049_1__concoct_068                          -2.101229
## 11049_1__concoct_084                          -4.844997
## 11049_1__concoct_129_sub                      -4.024016
## 11049_1__concoct_161_sub                       2.416930
##                          moore_1__BBG6442_22S000877 moore_2__BBG6443_21S000468
## 11049_1__concoct_009                     0.06895707                  0.4757257
## 11049_1__concoct_027_sub                 1.50729345                  2.3291147
## 11049_1__concoct_068                    -2.08620265                 -2.1613698
## 11049_1__concoct_084                    -5.10662754                 -5.5564881
## 11049_1__concoct_129_sub                -4.92430598                 -4.4578758
## 11049_1__concoct_161_sub                 0.88082899                  0.8210116
##                          moore_3__BBG6444_21S000469 moore_4__BBG6445_21S000470
## 11049_1__concoct_009                      0.3481784                  0.5932615
## 11049_1__concoct_027_sub                  2.5241204                  2.3941262
## 11049_1__concoct_068                     -2.5518468                 -2.4688657
## 11049_1__concoct_084                     -4.7490714                 -4.7447825
## 11049_1__concoct_129_sub                 -4.1692529                 -4.5537273
## 11049_1__concoct_161_sub                  0.9492199                  0.9344915
##                          Peart_1__BBG6430_21S000455 Peart_2__BBG6431_21S000456
## 11049_1__concoct_009                       1.984284                   1.909855
## 11049_1__concoct_027_sub                   3.100242                   2.788601
## 11049_1__concoct_068                      -2.243349                  -2.263342
## 11049_1__concoct_084                      -6.470183                  -5.670080
## 11049_1__concoct_129_sub                  -3.831125                  -3.996103
## 11049_1__concoct_161_sub                   2.463745                   2.467755
##                          Peart_3__BBG6432_21S000457 Peart_4__BBG6433_21S000458
## 11049_1__concoct_009                       2.291990                   1.883065
## 11049_1__concoct_027_sub                   3.046085                   2.891615
## 11049_1__concoct_068                      -2.023893                  -2.090912
## 11049_1__concoct_084                      -6.393341                  -5.919553
## 11049_1__concoct_129_sub                  -3.828392                  -4.310115
## 11049_1__concoct_161_sub                   2.392810                   2.569909
##                          taylor_1__BBG6426_22S000876
## 11049_1__concoct_009                       -1.942922
## 11049_1__concoct_027_sub                    2.903325
## 11049_1__concoct_068                       -1.701057
## 11049_1__concoct_084                       -5.228964
## 11049_1__concoct_129_sub                   -3.196669
## 11049_1__concoct_161_sub                    0.507778
##                          taylor_2__BBG6427_21S000453
## 11049_1__concoct_009                      -1.9394992
## 11049_1__concoct_027_sub                   3.2053383
## 11049_1__concoct_068                      -2.0339377
## 11049_1__concoct_084                      -5.7006993
## 11049_1__concoct_129_sub                  -3.5904861
## 11049_1__concoct_161_sub                   0.2935738
##                          taylor_3__BBG6428_21S000454
## 11049_1__concoct_009                      -1.6617500
## 11049_1__concoct_027_sub                   2.8833861
## 11049_1__concoct_068                      -2.0004176
## 11049_1__concoct_084                      -5.5870182
## 11049_1__concoct_129_sub                  -3.4275340
## 11049_1__concoct_161_sub                   0.3991546
##                          taylor_4__BBG6429_21S000075
## 11049_1__concoct_009                      -1.8730318
## 11049_1__concoct_027_sub                   3.5122215
## 11049_1__concoct_068                      -1.5448398
## 11049_1__concoct_084                      -5.1373882
## 11049_1__concoct_129_sub                  -3.3873014
## 11049_1__concoct_161_sub                   0.3713389
### IMPORTANT: use pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains only for MINT!!

# CLR transforming only within Swains - use this object for PCA
pMAGs_95ANI_phyloseq_clr_Swains_only <- microbiome::transform(pMAGs_95ANI_phyloseq_Swains_only, transform = "clr")
# This object pMAGs_95ANI_phyloseq_clr_Swains_only will be to validate the model

# Extracting the dataframe
MAGs_no_Swains <- as.data.frame(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@otu_table)
MAGs_no_Swains <- t(MAGs_no_Swains)
# Check dimensions of data
dim(MAGs_no_Swains)
## [1] 170 876
class(MAGs_no_Swains)
## [1] "matrix" "array"
mint.splsda.open.closed_no_Swains <- mint.splsda(X = MAGs_no_Swains,
                              Y = pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$Open_or_Closed_to_fishing,
                              study = pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$SECTOR_N_S,
                              ncomp = 10)
perf.mint.splsda.open.closed_no_Swains <- perf(mint.splsda.open.closed_no_Swains)
plot(perf.mint.splsda.open.closed_no_Swains)
Choosing the number of components in mint.splsda using perf() with LOGOCV to discriminate between reefs that are open or closed to fishing. Classification error rates (overall and balanced - BER) are represented on the y-axis with respect to the number of components on the x-axis for each prediction distance. Overall and balanced error rates show the same trend as the design is balanced (i.e. the same number of protected and non-protected reefs in each sampling trip). The plot shows that the error rate reaches a minimum with three dimensions with the centroids prediction distance. We therefore retained 3 PCs in downstream analysis.

Choosing the number of components in mint.splsda using perf() with LOGOCV to discriminate between reefs that are open or closed to fishing. Classification error rates (overall and balanced - BER) are represented on the y-axis with respect to the number of components on the x-axis for each prediction distance. Overall and balanced error rates show the same trend as the design is balanced (i.e. the same number of protected and non-protected reefs in each sampling trip). The plot shows that the error rate reaches a minimum with three dimensions with the centroids prediction distance. We therefore retained 3 PCs in downstream analysis.

Let’s see the overlap of selected features between MINT sPLS-DA models when study = Sampling_trip vs Sector.

# making sure that similar taxa are selected in MINT sPLS-DA models when I select TRIP or SECTOR as a study
mint.splsda.open.closed.trip.100 <- mint.splsda(X = MAGs,
                              Y = pMAGs_95ANI_phyloseq_clr@sam_data$Open_or_Closed_to_fishing,
                              study = pMAGs_95ANI_phyloseq_clr@sam_data$Sampling_trip,
                              keepX = c(100, 10),
                              ncomp = 2)
mint.splsda.open.closed.sector.100 <- mint.splsda(X = MAGs,
                              Y = pMAGs_95ANI_phyloseq_clr@sam_data$Open_or_Closed_to_fishing,
                              study = pMAGs_95ANI_phyloseq_clr@sam_data$SECTOR_N_S,
                              keepX = c(100, 10),
                              ncomp = 2)

# Extracting the 100 indicators
mint.splsda.open.closed.trip.100.vars <- selectVar(mint.splsda.open.closed.trip.100, comp = 1)$name
mint.splsda.open.closed.sector.100.vars <- selectVar(mint.splsda.open.closed.sector.100, comp = 1)$name

### Ready for a Venn diagram now:
# Find the intersection (shared features) between the two
shared_features <- intersect(mint.splsda.open.closed.trip.100.vars, mint.splsda.open.closed.sector.100.vars)

# Create a Venn diagram
venn.plot <- venn.diagram(
  x = list(
    "Trip" = mint.splsda.open.closed.trip.100.vars,
    "Sector" = mint.splsda.open.closed.sector.100.vars
  ),
  category.names = c("Trip", "Sector"),
  filename = NULL,  # Do not save to file, just plot it
  output = TRUE
)

# Plot the Venn diagram
grid.draw(venn.plot)

# If you want to see the number of shared features
cat("Number of shared features: ", length(shared_features), "\n")
## Number of shared features:  69

As the results are largely similar, we will continue with sector-specific MINT (sPLS-DA and sPLS) from now on.

Also checking the overlap between MINT sPLS-DA on 7 and 6 sectors (i.e., no Swains)

# making sure that similar taxa are selected in MINT sPLS-DA models when I select TRIP or SECTOR as a study
mint.splsda.open.closed.6sectors.100 <- mint.splsda(X = MAGs_no_Swains,
                              Y = pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$Open_or_Closed_to_fishing,
                              study = pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$SECTOR_N_S,
                              keepX = c(100, 10),
                              ncomp = 2)
mint.splsda.open.closed.7sectors.100 <- mint.splsda(X = MAGs_MINT,
                              Y = pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Open_or_Closed_to_fishing,
                              study = pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$SECTOR_N_S,
                              keepX = c(100, 10),
                              ncomp = 2)

# Extracting the 100 indicators
mint.splsda.open.closed.6sectors.100.vars <- selectVar(mint.splsda.open.closed.6sectors.100, comp = 1)$name
mint.splsda.open.closed.7sectors.100.vars <- selectVar(mint.splsda.open.closed.7sectors.100, comp = 1)$name

### Ready for a Venn diagram now:
# Find the intersection (shared features) between the two
shared_features <- intersect(mint.splsda.open.closed.6sectors.100.vars,
                             mint.splsda.open.closed.7sectors.100.vars)

# Create a Venn diagram
venn.plot <- venn.diagram(
  x = list(
    "MINT sPLS-DA no Swains" = mint.splsda.open.closed.6sectors.100.vars,
    "MINT sPLS-DA all sectors" = mint.splsda.open.closed.7sectors.100.vars
  ),
  category.names = c("6 sectors", "7 sectors"),
  filename = NULL,  # Do not save to file, just plot it
  output = TRUE
)

# Plot the Venn diagram
grid.draw(venn.plot)

# If you want to see the number of shared features
cat("Number of shared features: ", length(shared_features), "\n")
## Number of shared features:  84

Again, largely similar results, but we will present a model with all seven sectors in the final manuscript (even though the design is unbalanced in Swains, but this is not an issue for MINT)

perf.mint.splsda.open.closed.sector$global.error$BER
##         max.dist centroids.dist mahalanobis.dist
## comp1  0.2872243      0.2965664        0.2965664
## comp2  0.2956015      0.2823120        0.2988910
## comp3  0.3079292      0.2399875        0.3070269
## comp4  0.3792074      0.2868296        0.3562907
## comp5  0.4125877      0.2702506        0.4138158
## comp6  0.3964693      0.2745269        0.3888158
## comp7  0.3987061      0.2755138        0.4039693
## comp8  0.4161184      0.2726629        0.4152162
## comp9  0.4212281      0.2792419        0.4278916
## comp10 0.4204605      0.2792419        0.4382675

But it may also be interesting too see the stats on this within sectors - is the error higher in some sectors compared to the others?

# Initialize an empty list to store the results
study_errors_overall <- list()

# Loop through each study in the 'study.specific.error' section
for (study_name in names(perf.mint.splsda.open.closed.sector[["study.specific.error"]])) {
  # Extract the error rate for the current study
  study_error_overall <- perf.mint.splsda.open.closed.sector$study.specific.error[[study_name]]$overall
  
  # Add the study name as a column to the error data
  study_error_with_name_overall <- cbind(Study = study_name, study_error_overall)
  
  # Store the error data in the list
  study_errors_overall[[study_name]] <- study_error_with_name_overall
}

# Combine all study data into a single data frame
study_error_df_overall <- do.call(rbind, study_errors_overall)

# Display the table
knitr::kable(as.data.frame(study_error_df_overall), caption = "MINT sPLS-DA - error rate (centroids distance) across GBR sectors")
MINT sPLS-DA - error rate (centroids distance) across GBR sectors
Study max.dist centroids.dist mahalanobis.dist
comp1 01_Cape_Grenville 0.416666666666667 0.416666666666667 0.416666666666667
comp2 01_Cape_Grenville 0.541666666666667 0.375 0.541666666666667
comp3 01_Cape_Grenville 0.625 0.333333333333333 0.625
comp4 01_Cape_Grenville 0.541666666666667 0.375 0.458333333333333
comp5 01_Cape_Grenville 0.625 0.333333333333333 0.666666666666667
comp6 01_Cape_Grenville 0.541666666666667 0.333333333333333 0.541666666666667
comp7 01_Cape_Grenville 0.583333333333333 0.333333333333333 0.625
comp8 01_Cape_Grenville 0.583333333333333 0.333333333333333 0.583333333333333
comp9 01_Cape_Grenville 0.625 0.333333333333333 0.583333333333333
comp10 01_Cape_Grenville 0.625 0.333333333333333 0.625
comp1.1 02_Princess_Charlotte_bay 0.2 0.2 0.2
comp2.1 02_Princess_Charlotte_bay 0.6 0.2 0.6
comp3.1 02_Princess_Charlotte_bay 0.6 0.2 0.533333333333333
comp4.1 02_Princess_Charlotte_bay 0.866666666666667 0.2 0.933333333333333
comp5.1 02_Princess_Charlotte_bay 1 0.2 1
comp6.1 02_Princess_Charlotte_bay 0.933333333333333 0.266666666666667 1
comp7.1 02_Princess_Charlotte_bay 0.8 0.2 0.8
comp8.1 02_Princess_Charlotte_bay 0.8 0.2 0.733333333333333
comp9.1 02_Princess_Charlotte_bay 0.866666666666667 0.2 0.866666666666667
comp10.1 02_Princess_Charlotte_bay 0.933333333333333 0.2 0.933333333333333
comp1.2 03_Cairns 0.35 0.35 0.35
comp2.2 03_Cairns 0.05 0.25 0.05
comp3.2 03_Cairns 0.2 0.3 0.2
comp4.2 03_Cairns 0.35 0.3 0.35
comp5.2 03_Cairns 0.35 0.3 0.35
comp6.2 03_Cairns 0.3 0.3 0.3
comp7.2 03_Cairns 0.2 0.3 0.2
comp8.2 03_Cairns 0.25 0.3 0.25
comp9.2 03_Cairns 0.25 0.35 0.25
comp10.2 03_Cairns 0.15 0.35 0.2
comp1.3 04_Innisfail 0.0740740740740741 0.111111111111111 0.111111111111111
comp2.3 04_Innisfail 0.259259259259259 0.148148148148148 0.259259259259259
comp3.3 04_Innisfail 0.259259259259259 0.148148148148148 0.296296296296296
comp4.3 04_Innisfail 0.37037037037037 0.222222222222222 0.333333333333333
comp5.3 04_Innisfail 0.37037037037037 0.185185185185185 0.333333333333333
comp6.3 04_Innisfail 0.259259259259259 0.148148148148148 0.296296296296296
comp7.3 04_Innisfail 0.444444444444444 0.185185185185185 0.444444444444444
comp8.3 04_Innisfail 0.407407407407407 0.185185185185185 0.444444444444444
comp9.3 04_Innisfail 0.37037037037037 0.185185185185185 0.407407407407407
comp10.3 04_Innisfail 0.37037037037037 0.185185185185185 0.444444444444444
comp1.4 05_Townsville 0.303571428571429 0.303571428571429 0.303571428571429
comp2.4 05_Townsville 0.267857142857143 0.285714285714286 0.267857142857143
comp3.4 05_Townsville 0.285714285714286 0.232142857142857 0.285714285714286
comp4.4 05_Townsville 0.285714285714286 0.25 0.267857142857143
comp5.4 05_Townsville 0.285714285714286 0.25 0.285714285714286
comp6.4 05_Townsville 0.392857142857143 0.267857142857143 0.339285714285714
comp7.4 05_Townsville 0.339285714285714 0.267857142857143 0.339285714285714
comp8.4 05_Townsville 0.357142857142857 0.267857142857143 0.357142857142857
comp9.4 05_Townsville 0.357142857142857 0.267857142857143 0.357142857142857
comp10.4 05_Townsville 0.357142857142857 0.267857142857143 0.357142857142857
comp1.5 06_Swains 0.45 0.45 0.45
comp2.5 06_Swains 0.25 0.4 0.3
comp3.5 06_Swains 0.15 0.3 0.15
comp4.5 06_Swains 0.25 0.4 0.25
comp5.5 06_Swains 0.25 0.3 0.25
comp6.5 06_Swains 0.2 0.3 0.2
comp7.5 06_Swains 0.25 0.3 0.25
comp8.5 06_Swains 0.15 0.35 0.15
comp9.5 06_Swains 0.15 0.35 0.2
comp10.5 06_Swains 0.3 0.35 0.35
comp1.6 07_Capricorn_Bunker 0.285714285714286 0.321428571428571 0.321428571428571
comp2.6 07_Capricorn_Bunker 0.285714285714286 0.357142857142857 0.285714285714286
comp3.6 07_Capricorn_Bunker 0.214285714285714 0.285714285714286 0.214285714285714
comp4.6 07_Capricorn_Bunker 0.357142857142857 0.357142857142857 0.321428571428571
comp5.6 07_Capricorn_Bunker 0.428571428571429 0.357142857142857 0.464285714285714
comp6.6 07_Capricorn_Bunker 0.392857142857143 0.357142857142857 0.392857142857143
comp7.6 07_Capricorn_Bunker 0.428571428571429 0.357142857142857 0.428571428571429
comp8.6 07_Capricorn_Bunker 0.535714285714286 0.321428571428571 0.535714285714286
comp9.6 07_Capricorn_Bunker 0.535714285714286 0.321428571428571 0.571428571428571
comp10.6 07_Capricorn_Bunker 0.5 0.321428571428571 0.5
# Initialize an empty list to store the results
study_errors_overall_no_Swains <- list()

# Loop through each study in the 'study.specific.error' section
for (study_name in names(perf.mint.splsda.open.closed_no_Swains[["study.specific.error"]])) {
  # Extract the error rate for the current study
  study_error_overall <- perf.mint.splsda.open.closed_no_Swains$study.specific.error[[study_name]]$overall  # <- Fixed variable name
  
  # Add the study name as a column to the error data
  study_error_with_name_overall <- cbind(Study = study_name, study_error_overall)  # <- Fixed variable name
  
  # Store the error data in the list
  study_errors_overall_no_Swains[[study_name]] <- study_error_with_name_overall
}

# Combine all study data into a single data frame
study_error_df_overall_no_Swains <- do.call(rbind, study_errors_overall_no_Swains)

# Display the table
knitr::kable(as.data.frame(study_error_df_overall_no_Swains), caption = "MINT sPLS-DA - error rate (centroids distance) across six GBR sectors (Swains excluded)")
MINT sPLS-DA - error rate (centroids distance) across six GBR sectors (Swains excluded)
Study max.dist centroids.dist mahalanobis.dist
comp1 01_Cape_Grenville 0.416666666666667 0.416666666666667 0.416666666666667
comp2 01_Cape_Grenville 0.5 0.416666666666667 0.5
comp3 01_Cape_Grenville 0.583333333333333 0.375 0.5
comp4 01_Cape_Grenville 0.458333333333333 0.458333333333333 0.458333333333333
comp5 01_Cape_Grenville 0.625 0.375 0.583333333333333
comp6 01_Cape_Grenville 0.5 0.375 0.541666666666667
comp7 01_Cape_Grenville 0.541666666666667 0.375 0.583333333333333
comp8 01_Cape_Grenville 0.625 0.416666666666667 0.625
comp9 01_Cape_Grenville 0.583333333333333 0.416666666666667 0.625
comp10 01_Cape_Grenville 0.625 0.375 0.625
comp1.1 02_Princess_Charlotte_bay 0.2 0.2 0.2
comp2.1 02_Princess_Charlotte_bay 0.666666666666667 0.2 0.666666666666667
comp3.1 02_Princess_Charlotte_bay 0.533333333333333 0.2 0.533333333333333
comp4.1 02_Princess_Charlotte_bay 0.933333333333333 0.2 0.933333333333333
comp5.1 02_Princess_Charlotte_bay 1 0.2 1
comp6.1 02_Princess_Charlotte_bay 1 0.2 1
comp7.1 02_Princess_Charlotte_bay 1 0.266666666666667 1
comp8.1 02_Princess_Charlotte_bay 1 0.2 0.933333333333333
comp9.1 02_Princess_Charlotte_bay 1 0.2 0.866666666666667
comp10.1 02_Princess_Charlotte_bay 1 0.2 1
comp1.2 03_Cairns 0.35 0.35 0.35
comp2.2 03_Cairns 0.05 0.35 0.05
comp3.2 03_Cairns 0.25 0.3 0.25
comp4.2 03_Cairns 0.25 0.3 0.3
comp5.2 03_Cairns 0.35 0.3 0.35
comp6.2 03_Cairns 0.3 0.3 0.3
comp7.2 03_Cairns 0.4 0.3 0.35
comp8.2 03_Cairns 0.35 0.3 0.4
comp9.2 03_Cairns 0.4 0.35 0.45
comp10.2 03_Cairns 0.35 0.35 0.4
comp1.3 04_Innisfail 0.111111111111111 0.111111111111111 0.111111111111111
comp2.3 04_Innisfail 0.259259259259259 0.148148148148148 0.259259259259259
comp3.3 04_Innisfail 0.296296296296296 0.185185185185185 0.296296296296296
comp4.3 04_Innisfail 0.407407407407407 0.185185185185185 0.407407407407407
comp5.3 04_Innisfail 0.37037037037037 0.185185185185185 0.37037037037037
comp6.3 04_Innisfail 0.296296296296296 0.185185185185185 0.296296296296296
comp7.3 04_Innisfail 0.407407407407407 0.185185185185185 0.407407407407407
comp8.3 04_Innisfail 0.407407407407407 0.185185185185185 0.407407407407407
comp9.3 04_Innisfail 0.444444444444444 0.185185185185185 0.444444444444444
comp10.3 04_Innisfail 0.37037037037037 0.185185185185185 0.37037037037037
comp1.4 05_Townsville 0.303571428571429 0.303571428571429 0.303571428571429
comp2.4 05_Townsville 0.285714285714286 0.321428571428571 0.303571428571429
comp3.4 05_Townsville 0.285714285714286 0.267857142857143 0.267857142857143
comp4.4 05_Townsville 0.303571428571429 0.267857142857143 0.321428571428571
comp5.4 05_Townsville 0.285714285714286 0.285714285714286 0.303571428571429
comp6.4 05_Townsville 0.375 0.285714285714286 0.392857142857143
comp7.4 05_Townsville 0.375 0.303571428571429 0.410714285714286
comp8.4 05_Townsville 0.339285714285714 0.267857142857143 0.339285714285714
comp9.4 05_Townsville 0.339285714285714 0.267857142857143 0.339285714285714
comp10.4 05_Townsville 0.339285714285714 0.267857142857143 0.357142857142857
comp1.5 07_Capricorn_Bunker 0.321428571428571 0.321428571428571 0.321428571428571
comp2.5 07_Capricorn_Bunker 0.392857142857143 0.321428571428571 0.392857142857143
comp3.5 07_Capricorn_Bunker 0.285714285714286 0.321428571428571 0.285714285714286
comp4.5 07_Capricorn_Bunker 0.392857142857143 0.321428571428571 0.392857142857143
comp5.5 07_Capricorn_Bunker 0.428571428571429 0.321428571428571 0.428571428571429
comp6.5 07_Capricorn_Bunker 0.285714285714286 0.321428571428571 0.285714285714286
comp7.5 07_Capricorn_Bunker 0.357142857142857 0.321428571428571 0.357142857142857
comp8.5 07_Capricorn_Bunker 0.321428571428571 0.321428571428571 0.321428571428571
comp9.5 07_Capricorn_Bunker 0.392857142857143 0.321428571428571 0.392857142857143
comp10.5 07_Capricorn_Bunker 0.321428571428571 0.321428571428571 0.321428571428571
# Initialize an empty list to store the results
study_errors <- list()

# Loop through each study in the 'study.specific.error' section
for (study_name in names(perf.mint.splsda.open.closed.sector[["study.specific.error"]])) {
  # Extract the error rate for the current study
  study_error <- perf.mint.splsda.open.closed.sector$study.specific.error[[study_name]]$error.rate.class$centroids.dist
  
  # Add the study name as a column to the error data
  study_error_with_name <- cbind(Study = study_name, study_error)
  
  # Store the error data in the list
  study_errors[[study_name]] <- study_error_with_name
}

# Combine all study data into a single data frame
study_error_df <- do.call(rbind, study_errors)

# Display the table
knitr::kable(as.data.frame(study_error_df), caption = "MINT sPLS-DA - error rate (centroids distance) across GBR sectors, and separately for C and O")
MINT sPLS-DA - error rate (centroids distance) across GBR sectors, and separately for C and O
Study comp1 comp2 comp3 comp4 comp5 comp6 comp7 comp8 comp9 comp10
C 01_Cape_Grenville 0.583333333333333 0.583333333333333 0.5 0.583333333333333 0.5 0.5 0.5 0.5 0.5 0.5
O 01_Cape_Grenville 0.25 0.166666666666667 0.166666666666667 0.166666666666667 0.166666666666667 0.166666666666667 0.166666666666667 0.166666666666667 0.166666666666667 0.166666666666667
C.1 02_Princess_Charlotte_bay 0 0 0 0 0 0.125 0 0 0 0
O.1 02_Princess_Charlotte_bay 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429
C.2 03_Cairns 0.25 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.25 0.25
O.2 03_Cairns 0.416666666666667 0.333333333333333 0.416666666666667 0.416666666666667 0.416666666666667 0.416666666666667 0.416666666666667 0.416666666666667 0.416666666666667 0.416666666666667
C.3 04_Innisfail 0.133333333333333 0.133333333333333 0.133333333333333 0.2 0.133333333333333 0.133333333333333 0.133333333333333 0.133333333333333 0.133333333333333 0.133333333333333
O.3 04_Innisfail 0.0833333333333333 0.166666666666667 0.166666666666667 0.25 0.25 0.166666666666667 0.25 0.25 0.25 0.25
C.4 05_Townsville 0.392857142857143 0.392857142857143 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429
O.4 05_Townsville 0.214285714285714 0.178571428571429 0.0357142857142857 0.0714285714285714 0.0714285714285714 0.107142857142857 0.107142857142857 0.107142857142857 0.107142857142857 0.107142857142857
C.5 06_Swains 0.25 0.25 0 0.25 0.25 0.25 0.25 0.25 0.25 0.25
O.5 06_Swains 0.5 0.4375 0.375 0.4375 0.3125 0.3125 0.3125 0.375 0.375 0.375
C.6 07_Capricorn_Bunker 0.3125 0.375 0.25 0.375 0.375 0.375 0.375 0.375 0.375 0.375
O.6 07_Capricorn_Bunker 0.333333333333333 0.333333333333333 0.333333333333333 0.333333333333333 0.333333333333333 0.333333333333333 0.333333333333333 0.25 0.25 0.25
# Initialize an empty list to store the results
study_errors_no_Swains <- list()

# Loop through each study in the 'study.specific.error' section
for (study_name in names(perf.mint.splsda.open.closed_no_Swains[["study.specific.error"]])) {
  # Extract the error rate for the current study
  study_error <- perf.mint.splsda.open.closed_no_Swains$study.specific.error[[study_name]]$error.rate.class$centroids.dist
  
  # Add the study name as a column to the error data
  study_error_with_name_no_Swains <- cbind(Study = study_name, study_error)
  
  # Store the error data in the list
  study_errors_no_Swains[[study_name]] <- study_error_with_name_no_Swains
}

# Combine all study data into a single data frame
study_error_df_no_Swains <- do.call(rbind, study_errors_no_Swains)

# Display the table
knitr::kable(as.data.frame(study_error_df_no_Swains), caption = "MINT sPLS-DA - error rate (centroids distance) across GBR sectors (Swains excluded), and separately for C and O")
MINT sPLS-DA - error rate (centroids distance) across GBR sectors (Swains excluded), and separately for C and O
Study comp1 comp2 comp3 comp4 comp5 comp6 comp7 comp8 comp9 comp10
C 01_Cape_Grenville 0.583333333333333 0.583333333333333 0.5 0.583333333333333 0.5 0.5 0.5 0.5 0.5 0.5
O 01_Cape_Grenville 0.25 0.25 0.25 0.333333333333333 0.25 0.25 0.25 0.333333333333333 0.333333333333333 0.25
C.1 02_Princess_Charlotte_bay 0 0 0 0 0 0 0.125 0 0 0
O.1 02_Princess_Charlotte_bay 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429 0.428571428571429
C.2 03_Cairns 0.25 0.25 0.125 0.125 0.125 0.125 0.125 0.125 0.25 0.25
O.2 03_Cairns 0.416666666666667 0.416666666666667 0.416666666666667 0.416666666666667 0.416666666666667 0.416666666666667 0.416666666666667 0.416666666666667 0.416666666666667 0.416666666666667
C.3 04_Innisfail 0.0666666666666667 0.133333333333333 0.133333333333333 0.133333333333333 0.133333333333333 0.133333333333333 0.133333333333333 0.133333333333333 0.133333333333333 0.133333333333333
O.3 04_Innisfail 0.166666666666667 0.166666666666667 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
C.4 05_Townsville 0.392857142857143 0.357142857142857 0.392857142857143 0.392857142857143 0.392857142857143 0.392857142857143 0.392857142857143 0.392857142857143 0.392857142857143 0.392857142857143
O.4 05_Townsville 0.214285714285714 0.285714285714286 0.142857142857143 0.142857142857143 0.178571428571429 0.178571428571429 0.214285714285714 0.142857142857143 0.142857142857143 0.142857142857143
C.5 07_Capricorn_Bunker 0.3125 0.3125 0.3125 0.3125 0.3125 0.3125 0.3125 0.3125 0.3125 0.3125
O.5 07_Capricorn_Bunker 0.333333333333333 0.333333333333333 0.333333333333333 0.333333333333333 0.333333333333333 0.333333333333333 0.333333333333333 0.333333333333333 0.333333333333333 0.333333333333333

Tuning the number of features per dimension

We can choose the keepX parameter using the tune() function for a MINT object. The function performs LOGOCV for different values of test.keepX provided on each component, and no repeat argument is needed. Based on the mean classification error rate (overall error rate or BER) and a centroids distance, we output the optimal number of variables keepX to be included in the final model. This step was skipped and we retained 50 MAGs per each of the three dimensions.

# But in case I ever decide to do the tuning, this would be the script
tune.mint.splsda.open.closed.sector <- tune(X = MAGs_MINT,
                                     Y = as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Open_or_Closed_to_fishing),
                                     study = as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$SECTOR_N_S),
                                     ncomp = 5,
                                     test.keepX = seq(10, 500, 10),
                                     method = 'mint.splsda', #Specify the method
                                     measure = 'BER',
                                     dist = "centroids.dist")
# But in case I ever decide to do the tuning, this would be the script
tune.mint.splsda.open.closed.sector_no_Swains <- tune(X = MAGs_no_Swains,
                                     Y = as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$Open_or_Closed_to_fishing),
                                     study = as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$SECTOR_N_S),
                                     ncomp = 5,
                                     test.keepX = seq(10, 500, 10),
                                     method = 'mint.splsda', #Specify the method
                                     measure = 'BER',
                                     dist = "centroids.dist")
plot(tune.mint.splsda.open.closed.sector, sd = FALSE)
Tuning plot of the MINT sPLS-DA models with up to 5 components. Diamonds represent the optimal number of features on a given component. Balanced error rate found on the vertical axis and is the metric to be minimised.

Tuning plot of the MINT sPLS-DA models with up to 5 components. Diamonds represent the optimal number of features on a given component. Balanced error rate found on the vertical axis and is the metric to be minimised.

### Optimal nyumber of components
tune.mint.splsda.open.closed.sector$choice.ncomp
## $ncomp
## [1] 1
## 
## $values
##                               comp1     comp2     comp3     comp4     comp5
## 01_Cape_Grenville         0.4166667 0.3750000 0.3750000 0.3750000 0.3750000
## 02_Princess_Charlotte_bay 0.2142857 0.2142857 0.2142857 0.2142857 0.2142857
## 03_Cairns                 0.3333333 0.2708333 0.2708333 0.2708333 0.2708333
## 04_Innisfail              0.1500000 0.1500000 0.1833333 0.1833333 0.1833333
## 05_Townsville             0.2857143 0.2500000 0.2500000 0.2500000 0.2500000
## 06_Swains                 0.3750000 0.3125000 0.3437500 0.3750000 0.3437500
## 07_Capricorn_Bunker       0.3229167 0.3541667 0.3541667 0.3541667 0.3541667
### Optimal number of ffeatures per component
tune.mint.spls_da.optimal.keepX.sector <- tune.mint.splsda.open.closed.sector$choice.keepX # extract optimal values
tune.mint.spls_da.optimal.keepX.sector
## comp1 comp2 comp3 comp4 comp5 
##   350   180    10    10    20
plot(tune.mint.splsda.open.closed.sector_no_Swains, sd = FALSE)
Tuning plot of the MINT sPLS-DA models with up to 5 components. Diamonds represent the optimal number of features on a given component. Balanced error rate found on the vertical axis and is the metric to be minimised.

Tuning plot of the MINT sPLS-DA models with up to 5 components. Diamonds represent the optimal number of features on a given component. Balanced error rate found on the vertical axis and is the metric to be minimised.

### Optimal nyumber of components
# tune.mint.splsda.open.closed$choice.ncomp

### Optimal number of ffeatures per component
tune.mint.spls_da.optimal.keepX.sector_no_Swains <- tune.mint.splsda.open.closed.sector_no_Swains$choice.keepX # extract optimal values
tune.mint.spls_da.optimal.keepX.sector_no_Swains
## comp1 comp2 comp3 comp4 comp5 
##   420   270   190    10   250
tune.mint.splsda.open.closed.sector[["error.rate.class"]]
## $comp1
##   test.keepX.350
## C      0.3076923
## O      0.3030303
## 
## $comp2
##   test.keepX.180
## C      0.3076923
## O      0.2525253
## 
## $comp3
##   test.keepX.10
## C     0.3186813
## O     0.2626263
## 
## $comp4
##   test.keepX.10
## C     0.3186813
## O     0.2727273
## 
## $comp5
##   test.keepX.20
## C     0.3186813
## O     0.2626263
tune.mint.splsda.open.closed.sector_no_Swains[["error.rate.class"]]
## $comp1
##   test.keepX.420
## C      0.2988506
## O      0.2771084
## 
## $comp2
##   test.keepX.270
## C      0.2873563
## O      0.2891566
## 
## $comp3
##   test.keepX.190
## C      0.2988506
## O      0.2650602
## 
## $comp4
##   test.keepX.10
## C     0.2988506
## O     0.2650602
## 
## $comp5
##   test.keepX.250
## C      0.2758621
## O      0.2771084
final.mint.splsda.open.closed.sector <- mint.splsda(X = MAGs_MINT,
                                             Y = pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Open_or_Closed_to_fishing,
                                             keepX = tune.mint.spls_da.optimal.keepX.sector,
#                                             keepX = c(50, 50, 50), # Uncomment for arbitrary number of features
                                             study = pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$SECTOR_N_S,
                                             ncomp = 2) # based on the BER
## keepX is of length 5 while ncomp is 2 
## trimming keepX to c(350,180)
final.mint.splsda.open.closed.sector_no_Swains <- mint.splsda(X = MAGs_no_Swains,
                                             Y = pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$Open_or_Closed_to_fishing,
                                             keepX = tune.mint.spls_da.optimal.keepX.sector_no_Swains,
#                                             keepX = c(50, 50, 50), # Uncomment for arbitrary number of features
                                             study = pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$SECTOR_N_S,
                                             ncomp = 2) # based on the BER
## keepX is of length 5 while ncomp is 2 
## trimming keepX to c(420,270)
sample.plot.mint.splsda.open.closed.global <- plotIndiv(final.mint.splsda.open.closed.sector,
          study = "global",
          comp = c(1,2), # We can look into comp 3 too, but I think 2 dimensions are enough
          legend = TRUE,
          col.per.group = c("seagreen3", # Closed to fishing
                            "steelblue4"), # open to fishing
#          title = 'MINT sPLS-DA using IMOS GBR-MGD MAGs | PCs 1-2',
          subtitle = 'Reefs that are open or closed to fishing',
          ellipse = T,
          )
Sample plot from the MINT sPLS-DA performed on the IMOS-MGD seawater MAGs to identify microbes that discriminate between reefs that are open or closed to fishing. Samples (reef sites) are projected into the MINT sPLS-DA space spanned by the first two components, and coloured by their corresponding category reflecting reef protection level. Symbols indicate the membership to an LTMP trip/transect. Component 1 discriminates between the two reef categories.

Sample plot from the MINT sPLS-DA performed on the IMOS-MGD seawater MAGs to identify microbes that discriminate between reefs that are open or closed to fishing. Samples (reef sites) are projected into the MINT sPLS-DA space spanned by the first two components, and coloured by their corresponding category reflecting reef protection level. Symbols indicate the membership to an LTMP trip/transect. Component 1 discriminates between the two reef categories.

sample.plot.mint.splsda.open.closed.global_no_Swains <- plotIndiv(final.mint.splsda.open.closed.sector_no_Swains,
          study = "global",
          comp = c(1,2), # We can look into comp 3 too, but I think 2 dimensions are enough
          legend = TRUE,
          col.per.group = c("seagreen3", # Closed to fishing
                            "steelblue4"), # open to fishing
          title = 'MINT sPLS-DA | Training dataset on 6 sectors',
          subtitle = 'MINT sPLS-DA | Training dataset on 6 sectors',
          ellipse = T
#          pch = pch.vec
          )
sample.plot.mint.splsda.open.closed.partial.sector <- plotIndiv(final.mint.splsda.open.closed.sector,
          legend = TRUE,
          study = "all.partial",
          col.per.group = c("seagreen3", # Closed to fishing
                            "steelblue4"), # open to fishing
#          title = 'MINT sPLS-DA using IMOS GBR-MGD MAGs: Open or Closed to fishing',
          ellipse = F)

sample.plot.mint.splsda.open.closed.partial.sector_no_Swains <- plotIndiv(final.mint.splsda.open.closed.sector_no_Swains,
          legend = TRUE,
          study = "all.partial",
          col.per.group = c("seagreen3", # Closed to fishing
                            "steelblue4"), # open to fishing
#          title = 'MINT sPLS-DA using IMOS GBR-MGD MAGs: Open or Closed to fishing',
          ellipse = F)

Lastly, what about those spatiotemporal batch effects we observed in (s)PLS-DA?

plotIndiv(final.mint.splsda.open.closed.sector,
          study = "global",
          comp = c(1,2), # We can look into comp 3 too, but I think 2 dimensions are enough
          legend = TRUE,
          group = sample_data(pMAGs_95ANI_phyloseq_CLR_per_sector)$Sampling_trip,
          col.per.group =c("indianred", # Sampling trip 1
                "indianred4", # Sampling trip 2 
                "red3", # Sampling trip 3
                "slateblue"), # Sampling trip 4
          title = 'MINT sPLS-DA using IMOS GBR-MGD MAGs | PCs 1-2',
          subtitle = 'AIMS-LTMP trips', ellipse = T)

This plot shows that there is no longer clustering between the trips, suggesting we accounted for spatiotemporal batch effects.

Correlation circle plot

We can examine our molecular signature selected with MINT sPLS-DA. The correlation circle plot highlights the contribution of each selected MAG to each component (close to the large circle), and their correlation (clusters of variables).

# all gene names have the same first 10 characters, 
# shorten all the names to reduce visual clutter
plotVar(final.mint.splsda.open.closed.sector,
        var.names = list(MAGs.name.super.short),
        cutoff = 0.7,
        )
Correlation circle plot representing the MAGs selected by MINT sPLS-DA to discriminate between reefs that are open or closed to fishing, across the four sampling transects. We only show the MAGs selected by MINT sPLS-DA on components 1 and 2, and with a corr. cutoff = 0.8. This graphic should be interpreted in conjunction with the sample plot above - i.e. we observe a subset of seawater MAGs that are strongly correlated and positively associated to component 1 (positive values on the x-axis, on the right), which are likely to characterise the groups of reef sites that are open to fishing. We also observe a subset of seawater MAGs that are negatively associated to dimension 1 (x-axis, left) that may characterise reef sites that are protected/closed to fishing (and are negatively correlated to the previous group of MAGs).

Correlation circle plot representing the MAGs selected by MINT sPLS-DA to discriminate between reefs that are open or closed to fishing, across the four sampling transects. We only show the MAGs selected by MINT sPLS-DA on components 1 and 2, and with a corr. cutoff = 0.8. This graphic should be interpreted in conjunction with the sample plot above - i.e. we observe a subset of seawater MAGs that are strongly correlated and positively associated to component 1 (positive values on the x-axis, on the right), which are likely to characterise the groups of reef sites that are open to fishing. We also observe a subset of seawater MAGs that are negatively associated to dimension 1 (x-axis, left) that may characterise reef sites that are protected/closed to fishing (and are negatively correlated to the previous group of MAGs).

# all gene names have the same first 10 characters, 
# shorten all the names to reduce visual clutter
plotVar(final.mint.splsda.open.closed.sector_no_Swains,
        var.names = list(MAGs.name.super.short),
        cutoff = 0.7,
        )
Correlation circle plot representing the MAGs selected by MINT sPLS-DA to discriminate between reefs that are open or closed to fishing, across the four sampling transects. We only show the MAGs selected by MINT sPLS-DA on components 1 and 2, and with a corr. cutoff = 0.8. This graphic should be interpreted in conjunction with the sample plot above - i.e. we observe a subset of seawater MAGs that are strongly correlated and positively associated to component 1 (positive values on the x-axis, on the right), which are likely to characterise the groups of reef sites that are open to fishing. We also observe a subset of seawater MAGs that are negatively associated to dimension 1 (x-axis, left) that may characterise reef sites that are protected/closed to fishing (and are negatively correlated to the previous group of MAGs).

Correlation circle plot representing the MAGs selected by MINT sPLS-DA to discriminate between reefs that are open or closed to fishing, across the four sampling transects. We only show the MAGs selected by MINT sPLS-DA on components 1 and 2, and with a corr. cutoff = 0.8. This graphic should be interpreted in conjunction with the sample plot above - i.e. we observe a subset of seawater MAGs that are strongly correlated and positively associated to component 1 (positive values on the x-axis, on the right), which are likely to characterise the groups of reef sites that are open to fishing. We also observe a subset of seawater MAGs that are negatively associated to dimension 1 (x-axis, left) that may characterise reef sites that are protected/closed to fishing (and are negatively correlated to the previous group of MAGs).

Loading plots

The plotLoadings() function displays the coefficient weight of each selected MAG in each IMOS GBR-MGD transect and shows the agreement of the molecular signatures across LTMP trips. Colours indicate the reef class (open or closed to fishing) in which the mean expression value of each selected MAG is maximal. These plots should be interpreted jointly with MINT sPLS-DA sample plots.

loading.plots.open.closed.per.sector <- plotLoadings(final.mint.splsda.open.closed.sector,
             contrib = "max",
             method = 'mean',
             comp=1,
             legend = TRUE,
             legend.color = c("seagreen3", # Closed
                              "steelblue4"), # Open
             ndisplay = 60,
             name.var = MAGs.name.short,
             study="all.partial",
             title="Contribution on comp 1",
#             subtitle = paste("Study",1:4)
             )
loading.plots.open.closed.per.sector
loading.plots.open.closed.per.sector_no_Swains <- plotLoadings(final.mint.splsda.open.closed.sector_no_Swains,
             contrib = "max",
             method = 'mean',
             comp=1,
             legend = TRUE,
             legend.color = c("seagreen3", # Closed
                              "steelblue4"), # Open
             ndisplay = 60,
             name.var = MAGs.name.short,
             study="all.partial",
             title="Contribution on comp 1",
#             subtitle = paste("Study",1:4)
             )
final.mint.splsda.open.closed.sector_no_Swains

We can also look at the averaged contribution across MINT studies:

loading.plots.open.closed.across.sectors <- plotLoadings(final.mint.splsda.open.closed.sector,
             contrib = "max",
             method = 'mean',
             comp=1,
             legend = TRUE,
             legend.color = c("seagreen3", # Closed
                              "steelblue4"), # Open
             ndisplay = 60,
             name.var = MAGs.name.short,
#             study="all.partial",
             title="Contribution on comp 1",
#             subtitle = paste("Study",1:4)
             )
loading.plots.open.closed.across.sectors

Clustered Image Maps

The Clustered Image Map represents the enrichment levels of the MAG signature per sample. Here we use the default Euclidean distance and Complete linkage for the first component.

cols.open.closed <- c("seagreen3","steelblue4")
open.closed.cols <- palette(cols.open.closed)[as.numeric(as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Open_or_Closed_to_fishing))]

cols.open.closed <- c("seagreen3","steelblue4")
open.closed.cols <- palette(cols.open.closed)[as.numeric(as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Open_or_Closed_to_fishing))]

# Exporting the names of taxa now, and making them short - easier plotting!
MAGs.name.short <- left_join(otu_table(pMAGs_95ANI_phyloseq_CLR_per_sector) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU"),
                            tax_table(pMAGs_95ANI_phyloseq_CLR_per_sector) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU")) %>%
  tidyr::unite(taxonomy, c(Class, Order, Family, Genus, Species), sep = "; ") # Adding Taxonomy info
## Joining, by = "OTU"
MAGs.name.short <- as.character(MAGs.name.short$taxonomy)

cim(final.mint.splsda.open.closed.sector,
    comp = 1,
#    cutoff = 0.95,
    col.names = MAGs.name.short,
    margins=c(37, # bottom
              25), # right
    keysize = c(1, 0.4),
#    row.sideColors = color.mixo(as.numeric(as.factor(metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing))),
    row.names = T,
legend = list(color.mixo(as.numeric(as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Open_or_Closed_to_fishing))),
              title = "Reef protection level"),
    row.sideColors = open.closed.cols,
    title = "MINT sPLS-DA, component 1",
xlab = "Indicator MAGs that discriminate between take and no take zones",
ylab = "Reef sites")
Clustered Image Map of the MAGs selected by MINT sPLS-DA for component 1 only, to discriminate between reefs that are open or closed to fishing. A hierarchical clustering based on the MAG enrichment levels of the indicator MAGs on component 1, with reef sites in rows coloured according to protection level.

Clustered Image Map of the MAGs selected by MINT sPLS-DA for component 1 only, to discriminate between reefs that are open or closed to fishing. A hierarchical clustering based on the MAG enrichment levels of the indicator MAGs on component 1, with reef sites in rows coloured according to protection level.

cols.open.closed <- c("seagreen3","steelblue4")
open.closed.cols <- palette(cols.open.closed)[as.numeric(as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$Open_or_Closed_to_fishing))]

cols.open.closed <- c("seagreen3","steelblue4")
open.closed.cols <- palette(cols.open.closed)[as.numeric(as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$Open_or_Closed_to_fishing))]

# Exporting the names of taxa now, and making them short - easier plotting!
MAGs.name.short <- left_join(otu_table(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU"),
                            tax_table(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU")) %>%
  tidyr::unite(taxonomy, c(Class, Order, Family, Genus, Species), sep = "; ") # Adding Taxonomy info
## Joining, by = "OTU"
MAGs.name.short <- as.character(MAGs.name.short$taxonomy)

cim(final.mint.splsda.open.closed.sector_no_Swains,
    comp = 1,
#    cutoff = 0.95,
    col.names = MAGs.name.short,
    margins=c(37, # bottom
              25), # right
    keysize = c(1, 0.4),
#    row.sideColors = color.mixo(as.numeric(as.factor(metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing))),
    row.names = T,
legend = list(color.mixo(as.numeric(as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$Open_or_Closed_to_fishing))),
              title = "Reef protection level"),
    row.sideColors = open.closed.cols,
    title = "MINT sPLS-DA, component 1",
xlab = "Indicator MAGs that discriminate between take and no take zones",
ylab = "Reef sites")
Clustered Image Map of the MAGs selected by MINT sPLS-DA for component 1 only, to discriminate between reefs that are open or closed to fishing. A hierarchical clustering based on the MAG enrichment levels of the indicator MAGs on component 1, with reef sites in rows coloured according to protection level.

Clustered Image Map of the MAGs selected by MINT sPLS-DA for component 1 only, to discriminate between reefs that are open or closed to fishing. A hierarchical clustering based on the MAG enrichment levels of the indicator MAGs on component 1, with reef sites in rows coloured according to protection level.

# Exporting for RawGraphs
cols.open.closed <- c("seagreen3","steelblue4")
open.closed.cols <- palette(cols.open.closed)[as.numeric(as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Open_or_Closed_to_fishing))]

cols.open.closed <- c("seagreen3","steelblue4")
open.closed.cols <- palette(cols.open.closed)[as.numeric(as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Open_or_Closed_to_fishing))]

# Getting group assignments for the 160 MAGs selected on component 1 - info in loading plots
loading.plots.open.closed.all.MAGs.sectors <- plotLoadings(final.mint.splsda.open.closed.sector,
             contrib = "max",
             method = 'mean',
             comp=1,
             legend = TRUE,
             legend.color = c("seagreen3", # Closed
                              "steelblue4"), # Open
#             ndisplay = 30,
             name.var = MAGs.name.short,
             study="all.partial",
             title="Contribution on comp 1",
#             subtitle = paste("Study",1:4)
             )
loading.plots.rawgraphs.sectors <- loading.plots.open.closed.all.MAGs.sectors %>%
  as.data.frame() # converting to data frame
loading.plots.rawgraphs.sectors <- loading.plots.rawgraphs.sectors %>%
  dplyr::select(ends_with("GroupContrib")) %>% 
  rownames_to_column("OTU")

# I will need the names first - full taxonomy with MAG ID numbers
MAGs.name.full <- left_join(otu_table(pMAGs_95ANI_phyloseq_CLR_per_sector) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU"),
                            tax_table(pMAGs_95ANI_phyloseq_CLR_per_sector) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU")) %>%
  tidyr::unite(taxonomy, c(OTU, Domain, Phylum, Class, Order, Family, Genus, Species), sep = "; ") # Adding Taxonomy info
## Joining, by = "OTU"
MAGs.name.full <- as.character(MAGs.name.full$taxonomy)

# Saving as an R object
mint.spls.da.rawgraphs.sectors <- cim(final.mint.splsda.open.closed.sector,
    comp = 1,
#    cutoff = 0.95,
    col.names = MAGs.name.full,
    margins=c(37, # bottom
              25), # right
    keysize = c(1, 0.4),
transpose = T,
#    row.sideColors = color.mixo(as.numeric(as.factor(metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing))),
    row.names = T,
legend = list(color.mixo(as.numeric(as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Open_or_Closed_to_fishing))),
              title = "Reef protection level"),
    row.sideColors = open.closed.cols,
    title = "MINT sPLS-DA, component 1",
xlab = "Indicator MAGs that discriminate between take and no take zones",
ylab = "Reef sites")
# Making a final object for RawGraphs
rawgraphs.order.sectors <- mint.spls.da.rawgraphs.sectors$col.names %>% 
  as.data.frame() %>% 
  tidyr::separate(., col = ., into = c("OTU", "Domain", "Phylum", "Class", "Order", "Family", "Genus", "Species"), sep = "; ") # Separating again
rawgraphs_final.sectors <- left_join(rawgraphs.order.sectors, loading.plots.rawgraphs.sectors)

# Exporting :)
write.csv(rawgraphs_final.sectors, file = "/home/marko-terzin/Desktop/MINT_sPLS_DA_for_rawgraphs_sectors.csv", row.names = F, quote = F)
# Reordering to have the same order as in the MINT sPLS-DA heatmap
# Used the solution from here:
# https://syntaxfix.com/question/22528/how-do-you-specifically-order-ggplot2-x-axis-instead-of-alphabetical-order
group.contrib.order.sectors <- rawgraphs.order.sectors$OTU %>% 
  as.data.frame()
colnames(group.contrib.order.sectors) <- "OTU"
loading.plots.rawgraphs.sectors <- left_join(group.contrib.order.sectors, loading.plots.rawgraphs.sectors)

# And lastly, plotting group contrib as a heatmap
loading.plots.long.sectors <- pivot_longer(loading.plots.rawgraphs.sectors, colnames(loading.plots.rawgraphs.sectors[,2:8]))
# Plotting
ggplot(loading.plots.long.sectors,                                # Draw heatmap-like plot
       aes(y=factor(OTU, level = unique(loading.plots.rawgraphs.sectors$OTU)), # Ordering in the same order as on the cim heatmap
           x=name,
           fill = value)) +
  geom_tile() + # plot a heatmap
  scale_fill_manual(values = c("seagreen3", # No-take zones
                               "steelblue4")) + # Take zones
    labs(x = 'AIMS-LTMP sectors',
       y = "Indicator MAGs",
       title = 'Take vs. no-take zones') +
      theme(axis.text.x = element_text(angle = 90, hjust = 1, size = 12))
Saving as R object for rawgraphs.

Saving as R object for rawgraphs.

# Exporting for RawGraphs
cols.open.closed <- c("seagreen3","steelblue4")
open.closed.cols <- palette(cols.open.closed)[as.numeric(as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$Open_or_Closed_to_fishing))]

cols.open.closed <- c("seagreen3","steelblue4")
open.closed.cols <- palette(cols.open.closed)[as.numeric(as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains@sam_data$Open_or_Closed_to_fishing))]

# Getting group assignments for the 160 MAGs selected on component 1 - info in loading plots
loading.plots.open.closed.all.MAGs.sectors_no_Swains <- plotLoadings(final.mint.splsda.open.closed.sector_no_Swains,
             contrib = "max",
             method = 'mean',
             comp=1,
             legend = TRUE,
             legend.color = c("seagreen3", # Closed
                              "steelblue4"), # Open
#             ndisplay = 30,
             name.var = MAGs.name.short,
             study="all.partial",
             title="Contribution on comp 1",
#             subtitle = paste("Study",1:4)
             )
loading.plots.rawgraphs.sectors_no_Swains <- loading.plots.open.closed.all.MAGs.sectors_no_Swains %>%
  as.data.frame() # converting to data frame
loading.plots.rawgraphs.sectors_no_Swains <- loading.plots.rawgraphs.sectors_no_Swains %>%
  dplyr::select(ends_with("GroupContrib")) %>% 
  rownames_to_column("OTU")

# I will need the names first - full taxonomy with MAG ID numbers
MAGs.name.full <- left_join(otu_table(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU"),
                            tax_table(pMAGs_95ANI_phyloseq_CLR_per_sector_no_Swains) %>%
                              as.data.frame %>%
                              rownames_to_column("OTU")) %>%
  tidyr::unite(taxonomy, c(OTU, Domain, Phylum, Class, Order, Family, Genus, Species), sep = "; ") # Adding Taxonomy info
## Joining, by = "OTU"
MAGs.name.full <- as.character(MAGs.name.full$taxonomy)

# Saving as an R object
mint.spls.da.rawgraphs.sectors_no_Swains <- cim(final.mint.splsda.open.closed.sector_no_Swains,
    comp = 1,
#    cutoff = 0.95,
    col.names = MAGs.name.full,
    margins=c(37, # bottom
              25), # right
    keysize = c(1, 0.4),
transpose = T,
#    row.sideColors = color.mixo(as.numeric(as.factor(metadata_IMOS_MGD_MAGs$Open_or_Closed_to_fishing))),
    row.names = T,
legend = list(color.mixo(as.numeric(as.factor(pMAGs_95ANI_phyloseq_CLR_per_sector@sam_data$Open_or_Closed_to_fishing))),
              title = "Reef protection level"),
    row.sideColors = open.closed.cols,
    title = "MINT sPLS-DA, component 1",
xlab = "Indicator MAGs that discriminate between take and no take zones",
ylab = "Reef sites")
# Making a final object for RawGraphs
rawgraphs.order.sectors_no_Swains <- mint.spls.da.rawgraphs.sectors_no_Swains$col.names %>% 
  as.data.frame() %>% 
  tidyr::separate(., col = ., into = c("OTU", "Domain", "Phylum", "Class", "Order", "Family", "Genus", "Species"), sep = "; ") # Separating again
rawgraphs_final.sectors_no_Swains <- left_join(rawgraphs.order.sectors_no_Swains, loading.plots.rawgraphs.sectors_no_Swains)

# Exporting :)
write.csv(rawgraphs_final.sectors_no_Swains, file = "/home/marko-terzin/Desktop/MINT_sPLS_DA_for_rawgraphs_sectors_no_Swains.csv", row.names = F, quote = F)
# Reordering to have the same order as in the MINT sPLS-DA heatmap
# Used the solution from here:
# https://syntaxfix.com/question/22528/how-do-you-specifically-order-ggplot2-x-axis-instead-of-alphabetical-order
group.contrib.order.sectors_no_Swains <- rawgraphs.order.sectors_no_Swains$OTU %>% 
  as.data.frame()
colnames(group.contrib.order.sectors_no_Swains) <- "OTU"
loading.plots.rawgraphs.sectors_no_Swains <- left_join(group.contrib.order.sectors_no_Swains, loading.plots.rawgraphs.sectors_no_Swains)

# And lastly, plotting group contrib as a heatmap
loading.plots.long.sectors_no_Swains <- pivot_longer(loading.plots.rawgraphs.sectors_no_Swains, colnames(loading.plots.rawgraphs.sectors_no_Swains[,2:7]))
# Plotting
ggplot(loading.plots.long.sectors_no_Swains,                                # Draw heatmap-like plot
       aes(y=factor(OTU, level = unique(loading.plots.rawgraphs.sectors_no_Swains$OTU)), # Ordering in the same order as on the cim heatmap
           x=name,
           fill = value)) +
  geom_tile() + # plot a heatmap
  scale_fill_manual(values = c("seagreen3", # No-take zones
                               "steelblue4")) + # Take zones
    labs(x = '6 AIMS-LTMP sectors',
       y = "Indicator MAGs",
       title = 'Take vs. no-take zones') +
      theme(axis.text.x = element_text(angle = 90, hjust = 1, size = 12))
Saving as R object for rawgraphs.

Saving as R object for rawgraphs.

Performance of the MINT sPLS-DA model

Use of the auroc() function will yield a visualisation of classification performance when undergoing the LOGOCV procedure from above. The interpretation of this output may not be particularly insightful in relation to the performance evaluation of our methods, but can complement the statistical analysis. For example, the model’s classification of open vs. closed sites had ~78% accuracy in classifying open and closed reefs in their corresponding category.

MINT_sPLS_da_open_closed_model_performance.sectors <- auroc(final.mint.splsda.open.closed.sector,
                                                            roc.comp = 1,
                                                            print = FALSE)
ROC curve and AUC from the MINT sPLS-DA performed on the IMOS GBR-MGD MAGs (876 MAGs, dereplicated in dRep at 95% ANI) for global component 1 for the open vs. closed reefs comparison. Numerical outputs include the AUC (0.7831) and a Wilcoxon test p−value (8.489e-12) for open vs. closed reefs class comparison that are performed per component.

ROC curve and AUC from the MINT sPLS-DA performed on the IMOS GBR-MGD MAGs (876 MAGs, dereplicated in dRep at 95% ANI) for global component 1 for the open vs. closed reefs comparison. Numerical outputs include the AUC (0.7831) and a Wilcoxon test p−value (8.489e-12) for open vs. closed reefs class comparison that are performed per component.

MINT_sPLS_da_open_closed_model_performance.sectors$Comp1
##           AUC   p-value
## C vs O 0.7354 2.146e-08
MINT_sPLS_da_open_closed_model_performance.sectors_no_Swains <- auroc(final.mint.splsda.open.closed.sector_no_Swains,
                                                            roc.comp = 1,
                                                            print = FALSE)
ROC curve and AUC from the MINT sPLS-DA performed on the IMOS GBR-MGD MAGs (876 MAGs, dereplicated in dRep at 95% ANI) for global component 1 for the open vs. closed reefs comparison. Numerical outputs include the AUC (0.7831) and a Wilcoxon test p−value (8.489e-12) for open vs. closed reefs class comparison that are performed per component.

ROC curve and AUC from the MINT sPLS-DA performed on the IMOS GBR-MGD MAGs (876 MAGs, dereplicated in dRep at 95% ANI) for global component 1 for the open vs. closed reefs comparison. Numerical outputs include the AUC (0.7831) and a Wilcoxon test p−value (8.489e-12) for open vs. closed reefs class comparison that are performed per component.

MINT_sPLS_da_open_closed_model_performance.sectors_no_Swains$Comp1
##           AUC   p-value
## C vs O 0.7347 1.275e-07

Can we validate this on the Swains sector? Prediction on an external study

We use the predict() function to predict the class membership of new test samples from an external study - Swains. Specifically, wrain the MINT model on the remaining 6 GBR sectors, then predict on the Swains sector. This process exactly reflects the inner workings of the tune() and perf() functions using LOGOCV. Here during our model training on the six sectors, we will set the parameters (i.e. choose ncomp and keepX) as in the tuning steps previously, using the model final.mint.splsda.open.closed.sector_no_Swains.

# We predict on study 3
indiv.test <- which(study == "3")

# We train on the remaining studies, with pre-tuned parameters
mint.splsda.stem2 <- mint.splsda(X = X[-c(indiv.test), ],
Y = Y[-c(indiv.test)],
study = droplevels(study[-c(indiv.test)]),
ncomp = 1,
keepX = 30)
mint.predict.stem <- predict(mint.splsda.stem2, newdata = X[indiv.test, ],
dist = "centroids.dist",
study.test = factor(study[indiv.test]))

# Store class prediction with a model with 1 comp
indiv.prediction <- mint.predict.stem$class$centroids.dist[, 1]

# The confusion matrix compares the real subtypes with the predicted subtypes
conf.mat <- get.confusion_matrix(truth = Y[indiv.test],
predicted = indiv.prediction)
conf.mat
# =============================================
# MINT sPLS-DA Prediction on External Dataset (Swains)
# =============================================

# --------------------------------------------
# Step 1: Prepare the Swains test data (CLR-transformed)
# --------------------------------------------
# CLR transform (if not already done)
pMAGs_95ANI_phyloseq_clr_Swains_only <- microbiome::transform(pMAGs_95ANI_phyloseq_Swains_only, transform = "clr")

# Extract OTU table (MAGs) and transpose to samples x features
MAGs_Swains_only <- as.data.frame(
  pMAGs_95ANI_phyloseq_clr_Swains_only@otu_table
)
MAGs_Swains_only <- t(MAGs_Swains_only)

# 1. Extract TRUE labels (Open_or_Closed_to_fishing) from phyloseq
true_labels_Swains <- pMAGs_95ANI_phyloseq_clr_Swains_only@sam_data$Open_or_Closed_to_fishing
# 2. Ensure true_labels_Swains is a factor (if not already)
true_labels_Swains <- factor(true_labels_Swains)

# Ensure the feature names match the training data
# (If needed, align columns with the model's feature space)
MAGs_Swains_only <- MAGs_Swains_only[, colnames(final.mint.splsda.open.closed.sector_no_Swains$X)]

# --------------------------------------------
# Step 2: Define test indices (Swains samples)
# --------------------------------------------
study.test <- factor(rep("06_Swains", nrow(MAGs_Swains_only)))
# 5. Sync factor levels with training data (critical for MINT)
levels(study.test) <- levels(final.mint.splsda.open.closed.sector_no_Swains$study)

# --------------------------------------------
# Step 3: Predict on Swains using the pre-trained MINT model
# --------------------------------------------
mint.predict.Swains <- predict(
  final.mint.splsda.open.closed.sector_no_Swains,  # Your pre-trained model
  newdata = MAGs_Swains_only,                     # Swains test data
  dist = "centroids.dist",                        # Distance metric
  study.test = study.test          # Study assignment for test data
)

# --------------------------------------------
# Step 4: Extract predictions and evaluate
# --------------------------------------------
# Get predicted classes (using the first two components)
indiv.prediction <- mint.predict.Swains$class$centroids.dist[, 2]

# Confusion matrix (if true labels are available)
conf.mat <- get.confusion_matrix(
  truth = true_labels_Swains,           # True labels for Swains
  predicted = indiv.prediction     # Predicted labels
)

# Print confusion matrix
print(conf.mat)
##   predicted.as.C predicted.as.O
## C              4              0
## O              9              7
# Calculate accuracy
accuracy <- sum(diag(conf.mat)) / sum(conf.mat)
print(paste("Accuracy:", round(accuracy, 3)))
## [1] "Accuracy: 0.55"

Analysis for tre IMOS GBR-MGD database paper (Robbins et al. 2025) - we only want the top 60 most discriminatory

final.mint.splsda.open.closed.sector.DB_paper <- mint.splsda(X = MAGs,
                                             Y = pMAGs_95ANI_phyloseq_clr@sam_data$Open_or_Closed_to_fishing,
#                                             keepX = tune.mint.spls_da.optimal.keepX.sector,
                                             keepX = c(60, 10), # Uncomment for arbitrary number of features
                                             study = pMAGs_95ANI_phyloseq_clr@sam_data$SECTOR_N_S,
                                             ncomp = 2) # based on the BER
perf.final.mint.splsda.open.closed.sector.DB_paper <- perf(final.mint.splsda.open.closed.sector.DB_paper)
# Initialize an empty list to store the results
study_errors_overall <- list()

# Loop through each study in the 'study.specific.error' section
for (study_name in names(perf.final.mint.splsda.open.closed.sector.DB_paper[["study.specific.error"]])) {
  # Extract the error rate for the current study
  study_error_overall <- perf.final.mint.splsda.open.closed.sector.DB_paper$study.specific.error[[study_name]]$overall
  
  # Add the study name as a column to the error data
  study_error_with_name_overall <- cbind(Study = study_name, study_error_overall)
  
  # Store the error data in the list
  study_errors_overall[[study_name]] <- study_error_with_name_overall
}

# Combine all study data into a single data frame
study_error_df_overall <- do.call(rbind, study_errors_overall)

# Display the table
knitr::kable(as.data.frame(study_error_df_overall), caption = "MINT sPLS-DA - error rate (centroids distance) across GBR sectors")
MINT sPLS-DA - error rate (centroids distance) across GBR sectors
Study max.dist centroids.dist mahalanobis.dist
comp1 01_Cape_Grenville 0.5 0.541666666666667 0.541666666666667
comp2 01_Cape_Grenville 0.583333333333333 0.5 0.583333333333333
comp1.1 02_Princess_Charlotte_bay 0.4 0.4 0.4
comp2.1 02_Princess_Charlotte_bay 0.733333333333333 0.4 0.733333333333333
comp1.2 03_Cairns 0.3 0.3 0.3
comp2.2 03_Cairns 0.35 0.35 0.4
comp1.3 04_Innisfail 0.148148148148148 0.148148148148148 0.148148148148148
comp2.3 04_Innisfail 0.185185185185185 0.148148148148148 0.185185185185185
comp1.4 05_Townsville 0.25 0.25 0.25
comp2.4 05_Townsville 0.285714285714286 0.25 0.285714285714286
comp1.5 06_Swains 0.5 0.5 0.5
comp2.5 06_Swains 0.4 0.5 0.4
comp1.6 07_Capricorn_Bunker 0.5 0.535714285714286 0.535714285714286
comp2.6 07_Capricorn_Bunker 0.428571428571429 0.535714285714286 0.392857142857143
# Initialize an empty list to store the results
study_errors <- list()

# Loop through each study in the 'study.specific.error' section
for (study_name in names(perf.final.mint.splsda.open.closed.sector.DB_paper[["study.specific.error"]])) {
  # Extract the error rate for the current study
  study_error <- perf.final.mint.splsda.open.closed.sector.DB_paper$study.specific.error[[study_name]]$error.rate.class$centroids.dist
  
  # Add the study name as a column to the error data
  study_error_with_name <- cbind(Study = study_name, study_error)
  
  # Store the error data in the list
  study_errors[[study_name]] <- study_error_with_name
}

# Combine all study data into a single data frame
study_error_df <- do.call(rbind, study_errors)

# Display the table
knitr::kable(as.data.frame(study_error_df), caption = "MINT sPLS-DA - error rate (centroids distance) across GBR sectors, and separately for C and O")
MINT sPLS-DA - error rate (centroids distance) across GBR sectors, and separately for C and O
Study comp1 comp2
C 01_Cape_Grenville 0.583333333333333 0.5
O 01_Cape_Grenville 0.5 0.5
C.1 02_Princess_Charlotte_bay 0.375 0.375
O.1 02_Princess_Charlotte_bay 0.428571428571429 0.428571428571429
C.2 03_Cairns 0.125 0.25
O.2 03_Cairns 0.416666666666667 0.416666666666667
C.3 04_Innisfail 0.2 0.2
O.3 04_Innisfail 0.0833333333333333 0.0833333333333333
C.4 05_Townsville 0.321428571428571 0.357142857142857
O.4 05_Townsville 0.178571428571429 0.142857142857143
C.5 06_Swains 0.25 0.25
O.5 06_Swains 0.5625 0.5625
C.6 07_Capricorn_Bunker 0.5 0.5
O.6 07_Capricorn_Bunker 0.583333333333333 0.583333333333333
# Is there a disconnect between the value I see here and in those mixOmics tuning plots? If yes, check if that is normal or weird
final.mint.splsda.open.closed.sector.DB_paper_model_performance <- auroc(final.mint.splsda.open.closed.sector.DB_paper, roc.comp = 1, print = FALSE)
final.mint.splsda.open.closed.sector.DB_paper_model_performance$Comp1
plotIndiv(final.mint.splsda.open.closed.sector.DB_paper,
          study = "global",
          comp = c(1,2), # We can look into comp 3 too, but I think 2 dimensions are enough
          legend = TRUE,
          col.per.group = c("seagreen3", # Closed to fishing
                            "steelblue4"), # open to fishing
          title = 'MINT sPLS-DA using IMOS GBR-MGD MAGs | PCs 1-2',
          subtitle = 'Reefs that are open or closed to fishing', ellipse = T)
# Since Steve asked me NOT to plot the sectors as symbols, I had to plot it externally in ggplot2, and not using mixOMics
variates_data <- as.data.frame(final.mint.splsda.open.closed.sector.DB_paper$variates$X)
variates_data$Group <- final.mint.splsda.open.closed.sector.DB_paper$Y

# Flom the previous plot, adding manually how much variance is explained on MINT sPLS-DA dimensions 1 and 2
explained_var1 <- 0.23 # Replace with actual value for comp1
explained_var2 <- 0.05 # Replace with actual value for comp2

ggplot(variates_data, aes(x = comp1, y = comp2, color = Group, fill = Group)) +
  geom_point() +
  stat_ellipse(aes(color = Group), geom = "path", linewidth = 1) + # Change to "path" for lines
#  stat_ellipse(geom = "polygon", alpha = 0.1, aes(fill = factor(Group)), color = NA) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "black", alpha = 0.3) +
  geom_vline(xintercept = 0, linetype = "dashed", color = "black", alpha = 0.3) +
  scale_color_manual(values = c("seagreen3", "steelblue4")) + # Coloring the points
  scale_fill_manual(values = c("seagreen3", "steelblue4")) + # Coloring the ellipses
  labs(x = paste('X-variate 1 (Variance Explained: ', explained_var1 * 100, '%)', sep = ''),
       y = paste('X-variate 2 (Variance Explained: ', explained_var2 * 100, '%)', sep = ''),
       title = 'MINT sPLS-DA using the 876 IMOS GBR-MGD pMAGs (95% ANI) | PCs 1-2',
       subtitle = 'top 60 most discriminatory pMAGs') +
  theme_minimal()
loading.plots.open.closed.per.sector.Steve <- plotLoadings(final.mint.splsda.open.closed.sector.DB_paper,
             contrib = "max",
             method = 'mean',
             comp=1,
             legend = TRUE,
             legend.color = c("seagreen3", # Closed
                              "steelblue4"), # Open
#             ndisplay = 60,
             name.var = MAGs.name.short,
             study="all.partial",
             title="Contribution on comp 1",
#             subtitle = paste("Study",1:4)
             )
loading.plots.open.closed.per.sector.Steve

We can also look at the averaged contribution across MINT studies (sectors):

loading.plots.open.closed.across.sectors.DB <- plotLoadings(final.mint.splsda.open.closed.sector.DB_paper,
             contrib = "max",
             method = 'mean',
             comp=1,
             legend = TRUE,
             legend.color = c("seagreen3", # Closed
                              "steelblue4"), # Open
             ndisplay = 60,
             name.var = MAGs.name.short,
#             study="all.partial",
             title="Contribution on comp 1",
#             subtitle = paste("Study",1:4)
             )
loading.plots.open.closed.across.sectors.DB

Saving the R object (for downstream analysis)

save.image(file = "/home/marko-terzin/Documents/PhD/Thesis/Chapter_3_IMOS-MGD_MAGs/cleaned_code/Figure_2/Figure_2.RData")

The final map (Fig. 2) was created in Inkscape.